Ising model in half-space: A series of phase transitions in low magnetic fields View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2007-11

AUTHORS

A. G. Basuev

ABSTRACT

For the Ising model in half-space at low temperatures and for the “unstable boundary condition,” we prove that for each value of the external magnetic field μ, there exists a spin layer of thickness q(μ) adjacent to the substrate such that the mean spin is close to −1 inside this layer and close to +1 outside it. As μ decreases, the thickness of the (−1)-spin layer changes jumpwise by unity at the points μq, and q(μ) → ∞ as μ → +0. At the discontinuity points μq of q(μ), two surface phases coexist. The surface free energy is piecewise analytic in the domain Re μ > 0 and at low temperatures. We consider the Ising model in half-space with an arbitrary external field in the zeroth layer and investigate the corresponding phase diagram. We prove Antonov’s rule and construct the equation of state in lower orders with the precision of x7, x = e−7ɛ. In particular, with this precision, we find the points of coexistence of the phases 0, 1, 2 and the phases 0, 2, 3, where the phase numbers correspond to the height of the layer of unstable spins over the substrate. More... »

PAGES

1539-1574

References to SciGraph publications

  • 1987-06. Phase diagram of the half-infinite ising model in JOURNAL OF STATISTICAL PHYSICS
  • 1979-02. Non-translation invariant Gibbs states with coexisting phases in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1979-02. Non-translation invariant Gibbs states with coexisting phases in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1975-02. Interface sharpness in the Ising system in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2004-05. Entropic repulsion of an interface in an external field in PROBABILITY THEORY AND RELATED FIELDS
  • 1986-03. Random surfaces in statistical mechanics: Roughening, rounding, wetting,... in JOURNAL OF STATISTICAL PHYSICS
  • 1979-10. Non-translation invariant Gibbs states with coexisting phases III: Analyticity properties in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1984-12. An alternate version of Pirogov-Sinai theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1994-02. Layering transition in SOS model with external magnetic field in JOURNAL OF STATISTICAL PHYSICS
  • 1977-06. Coexistence of phases in Ising ferromagnets in JOURNAL OF STATISTICAL PHYSICS
  • 1994-10. For 2-D lattice spin systems weak mixing implies strong mixing in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1983-10. Surface tension and phase coexistence for general lattice systems in JOURNAL OF STATISTICAL PHYSICS
  • 1987-03. Semi-infinite Ising model in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1975-12. Phase diagrams of classical lattice systems in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1988-09. Small-parameter series for the surface tension in a lattice model in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2002-06. Phase Diagram of Horizontally Invariant Gibbs States for Lattice Models in ANNALES HENRI POINCARÉ
  • 1984-03. Walks, walls, wetting, and melting in JOURNAL OF STATISTICAL PHYSICS
  • 1985-07. Hamiltonian of the phase separation border and phase transitions of the first kind. I in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1984-02. Complete phase diagrams with respect to external fields at low temperatures for models with nearest-neighbor interaction in the case of a finite or countable number of ground states in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1988-02. Rigid interfaces for lattice models at low temperatures in JOURNAL OF STATISTICAL PHYSICS
  • 1993-09. Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory in JOURNAL OF STATISTICAL PHYSICS
  • 2003-10. Surface Tension and Wulff Shape for a Lattice Model without Spin Flip Symmetry in ANNALES HENRI POINCARÉ
  • 1974-06. GHS and other inequalities in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1988-12. Analyticity properties of the surface free energy of the Ising model in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1980-05. Translation invariance and instability of phase coexistence in the two dimensional Ising system in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1987-09. Semi-infinite Ising model in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1986-03. Uniqueness and half-space nonuniqueness of gibbs states in Czech models in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1995-06. Complete analyticity for 2D Ising completed in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1996-02. On the layering transition of an SOS surface interacting with a wall. I. Equilibrium results in JOURNAL OF STATISTICAL PHYSICS
  • 1998-02. Finite-Volume Glauber Dynamics in a Small Magnetic Field in JOURNAL OF STATISTICAL PHYSICS
  • 1997-11. Exponential Relaxation of Glauber Dynamics with Some Special Boundary Conditions in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11232-007-0132-y

    DOI

    http://dx.doi.org/10.1007/s11232-007-0132-y

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1046811838


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0912", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Materials Engineering", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/09", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Engineering", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Saint-Petersburg State University of Technology and Design", 
              "id": "https://www.grid.ac/institutes/grid.445971.a", 
              "name": [
                "Saint-Petersburg State University of Technology and Design, St. Petersburg, Russia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Basuev", 
            "givenName": "A. G.", 
            "id": "sg:person.012424526446.93", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012424526446.93"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s00023-002-8616-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002783367", 
              "https://doi.org/10.1007/s00023-002-8616-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01018227", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007254359", 
              "https://doi.org/10.1007/bf01018227"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01217679", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011394911", 
              "https://doi.org/10.1007/bf01217679"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01224133", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012609545", 
              "https://doi.org/10.1007/bf01224133"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01224133", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012609545", 
              "https://doi.org/10.1007/bf01224133"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01017040", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012762935", 
              "https://doi.org/10.1007/bf01017040"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01009436", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015161718", 
              "https://doi.org/10.1007/bf01009436"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02188570", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016177871", 
              "https://doi.org/10.1007/bf02188570"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02188570", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016177871", 
              "https://doi.org/10.1007/bf02188570"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01152284", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016213776", 
              "https://doi.org/10.1007/bf01152284"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01152284", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016213776", 
              "https://doi.org/10.1007/bf01152284"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01009748", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017102814", 
              "https://doi.org/10.1007/bf01009748"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01206157", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018998981", 
              "https://doi.org/10.1007/bf01206157"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01206157", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018998981", 
              "https://doi.org/10.1007/bf01206157"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1214/154957806000000050", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019455710"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01212295", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021254136", 
              "https://doi.org/10.1007/bf01212295"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02099735", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024189378", 
              "https://doi.org/10.1007/bf02099735"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02099735", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024189378", 
              "https://doi.org/10.1007/bf02099735"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00440-003-0328-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025882267", 
              "https://doi.org/10.1007/s00440-003-0328-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00440-003-0328-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025882267", 
              "https://doi.org/10.1007/s00440-003-0328-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreve.66.056117", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027507418"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreve.66.056117", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027507418"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01646608", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029746508", 
              "https://doi.org/10.1007/bf01646608"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01646608", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029746508", 
              "https://doi.org/10.1007/bf01646608"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01646608", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029746508", 
              "https://doi.org/10.1007/bf01646608"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01197744", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031854114", 
              "https://doi.org/10.1007/bf01197744"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01197744", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031854114", 
              "https://doi.org/10.1007/bf01197744"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01017924", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033570166", 
              "https://doi.org/10.1007/bf01017924"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01017924", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033570166", 
              "https://doi.org/10.1007/bf01017924"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002200050203", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034537827", 
              "https://doi.org/10.1007/s002200050203"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01016860", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035327444", 
              "https://doi.org/10.1007/bf01016860"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02179794", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037124056", 
              "https://doi.org/10.1007/bf02179794"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02179794", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037124056", 
              "https://doi.org/10.1007/bf02179794"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01614092", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037382141", 
              "https://doi.org/10.1007/bf01614092"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01942696", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039238256", 
              "https://doi.org/10.1007/bf01942696"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01942696", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039238256", 
              "https://doi.org/10.1007/bf01942696"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01197743", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040695034", 
              "https://doi.org/10.1007/bf01197743"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01197743", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040695034", 
              "https://doi.org/10.1007/bf01197743"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01206148", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042008012", 
              "https://doi.org/10.1007/bf01206148"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01048183", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044165425", 
              "https://doi.org/10.1007/bf01048183"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01026500", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045447468", 
              "https://doi.org/10.1007/bf01026500"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00023-003-0149-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045457993", 
              "https://doi.org/10.1007/s00023-003-0149-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02108338", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046653185", 
              "https://doi.org/10.1007/bf02108338"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02108338", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046653185", 
              "https://doi.org/10.1007/bf02108338"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1023249608957", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046727891", 
              "https://doi.org/10.1023/a:1023249608957"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01197448", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047011008", 
              "https://doi.org/10.1007/bf01197448"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01197448", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047011008", 
              "https://doi.org/10.1007/bf01197448"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01040127", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047807510", 
              "https://doi.org/10.1007/bf01040127"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01040127", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047807510", 
              "https://doi.org/10.1007/bf01040127"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01010444", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049418892", 
              "https://doi.org/10.1007/bf01010444"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.434402", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058012433"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/revmodphys.57.827", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060839079"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/revmodphys.57.827", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060839079"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/1117073", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062866541"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1209/0295-5075/3/7/012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064230474"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2007-11", 
        "datePublishedReg": "2007-11-01", 
        "description": "For the Ising model in half-space at low temperatures and for the \u201cunstable boundary condition,\u201d we prove that for each value of the external magnetic field \u03bc, there exists a spin layer of thickness q(\u03bc) adjacent to the substrate such that the mean spin is close to \u22121 inside this layer and close to +1 outside it. As \u03bc decreases, the thickness of the (\u22121)-spin layer changes jumpwise by unity at the points \u03bcq, and q(\u03bc) \u2192 \u221e as \u03bc \u2192 +0. At the discontinuity points \u03bcq of q(\u03bc), two surface phases coexist. The surface free energy is piecewise analytic in the domain Re \u03bc > 0 and at low temperatures. We consider the Ising model in half-space with an arbitrary external field in the zeroth layer and investigate the corresponding phase diagram. We prove Antonov\u2019s rule and construct the equation of state in lower orders with the precision of x7, x = e\u22127\u025b. In particular, with this precision, we find the points of coexistence of the phases 0, 1, 2 and the phases 0, 2, 3, where the phase numbers correspond to the height of the layer of unstable spins over the substrate.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s11232-007-0132-y", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1327888", 
            "issn": [
              "0040-5779", 
              "2305-3135"
            ], 
            "name": "Theoretical and Mathematical Physics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "153"
          }
        ], 
        "name": "Ising model in half-space: A series of phase transitions in low magnetic fields", 
        "pagination": "1539-1574", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "defe4c7f09aaad847657897c77a596d1648f510ff77ae5a6eb957c87741d438f"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s11232-007-0132-y"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1046811838"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s11232-007-0132-y", 
          "https://app.dimensions.ai/details/publication/pub.1046811838"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T20:00", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8681_00000524.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2Fs11232-007-0132-y"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s11232-007-0132-y'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s11232-007-0132-y'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11232-007-0132-y'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11232-007-0132-y'


     

    This table displays all metadata directly associated to this object as RDF triples.

    203 TRIPLES      21 PREDICATES      64 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s11232-007-0132-y schema:about anzsrc-for:09
    2 anzsrc-for:0912
    3 schema:author N56263005c3f64794b4d7763d1ebd3989
    4 schema:citation sg:pub.10.1007/bf01009436
    5 sg:pub.10.1007/bf01009748
    6 sg:pub.10.1007/bf01010444
    7 sg:pub.10.1007/bf01016860
    8 sg:pub.10.1007/bf01017040
    9 sg:pub.10.1007/bf01017924
    10 sg:pub.10.1007/bf01018227
    11 sg:pub.10.1007/bf01026500
    12 sg:pub.10.1007/bf01040127
    13 sg:pub.10.1007/bf01048183
    14 sg:pub.10.1007/bf01152284
    15 sg:pub.10.1007/bf01197448
    16 sg:pub.10.1007/bf01197743
    17 sg:pub.10.1007/bf01197744
    18 sg:pub.10.1007/bf01206148
    19 sg:pub.10.1007/bf01206157
    20 sg:pub.10.1007/bf01212295
    21 sg:pub.10.1007/bf01217679
    22 sg:pub.10.1007/bf01224133
    23 sg:pub.10.1007/bf01614092
    24 sg:pub.10.1007/bf01646608
    25 sg:pub.10.1007/bf01942696
    26 sg:pub.10.1007/bf02099735
    27 sg:pub.10.1007/bf02108338
    28 sg:pub.10.1007/bf02179794
    29 sg:pub.10.1007/bf02188570
    30 sg:pub.10.1007/s00023-002-8616-7
    31 sg:pub.10.1007/s00023-003-0149-1
    32 sg:pub.10.1007/s002200050203
    33 sg:pub.10.1007/s00440-003-0328-5
    34 sg:pub.10.1023/a:1023249608957
    35 https://doi.org/10.1063/1.434402
    36 https://doi.org/10.1103/physreve.66.056117
    37 https://doi.org/10.1103/revmodphys.57.827
    38 https://doi.org/10.1137/1117073
    39 https://doi.org/10.1209/0295-5075/3/7/012
    40 https://doi.org/10.1214/154957806000000050
    41 schema:datePublished 2007-11
    42 schema:datePublishedReg 2007-11-01
    43 schema:description For the Ising model in half-space at low temperatures and for the “unstable boundary condition,” we prove that for each value of the external magnetic field μ, there exists a spin layer of thickness q(μ) adjacent to the substrate such that the mean spin is close to −1 inside this layer and close to +1 outside it. As μ decreases, the thickness of the (−1)-spin layer changes jumpwise by unity at the points μq, and q(μ) → ∞ as μ → +0. At the discontinuity points μq of q(μ), two surface phases coexist. The surface free energy is piecewise analytic in the domain Re μ > 0 and at low temperatures. We consider the Ising model in half-space with an arbitrary external field in the zeroth layer and investigate the corresponding phase diagram. We prove Antonov’s rule and construct the equation of state in lower orders with the precision of x7, x = e−7ɛ. In particular, with this precision, we find the points of coexistence of the phases 0, 1, 2 and the phases 0, 2, 3, where the phase numbers correspond to the height of the layer of unstable spins over the substrate.
    44 schema:genre research_article
    45 schema:inLanguage en
    46 schema:isAccessibleForFree false
    47 schema:isPartOf N2146f67faff44d6fa20fcbc88cbcef7e
    48 N9b588c84d6a946019d17dcf32b46ce6c
    49 sg:journal.1327888
    50 schema:name Ising model in half-space: A series of phase transitions in low magnetic fields
    51 schema:pagination 1539-1574
    52 schema:productId N18af4a13db8645b79686322dda0b96f0
    53 N19f02feac64a4cba91c4ea85ce5c8512
    54 N3e6b5c182868471daecaeea70c9673a0
    55 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046811838
    56 https://doi.org/10.1007/s11232-007-0132-y
    57 schema:sdDatePublished 2019-04-10T20:00
    58 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    59 schema:sdPublisher N5d0a0482f9994c63807d20eb67d761a2
    60 schema:url http://link.springer.com/10.1007%2Fs11232-007-0132-y
    61 sgo:license sg:explorer/license/
    62 sgo:sdDataset articles
    63 rdf:type schema:ScholarlyArticle
    64 N18af4a13db8645b79686322dda0b96f0 schema:name doi
    65 schema:value 10.1007/s11232-007-0132-y
    66 rdf:type schema:PropertyValue
    67 N19f02feac64a4cba91c4ea85ce5c8512 schema:name readcube_id
    68 schema:value defe4c7f09aaad847657897c77a596d1648f510ff77ae5a6eb957c87741d438f
    69 rdf:type schema:PropertyValue
    70 N2146f67faff44d6fa20fcbc88cbcef7e schema:volumeNumber 153
    71 rdf:type schema:PublicationVolume
    72 N3e6b5c182868471daecaeea70c9673a0 schema:name dimensions_id
    73 schema:value pub.1046811838
    74 rdf:type schema:PropertyValue
    75 N56263005c3f64794b4d7763d1ebd3989 rdf:first sg:person.012424526446.93
    76 rdf:rest rdf:nil
    77 N5d0a0482f9994c63807d20eb67d761a2 schema:name Springer Nature - SN SciGraph project
    78 rdf:type schema:Organization
    79 N9b588c84d6a946019d17dcf32b46ce6c schema:issueNumber 2
    80 rdf:type schema:PublicationIssue
    81 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
    82 schema:name Engineering
    83 rdf:type schema:DefinedTerm
    84 anzsrc-for:0912 schema:inDefinedTermSet anzsrc-for:
    85 schema:name Materials Engineering
    86 rdf:type schema:DefinedTerm
    87 sg:journal.1327888 schema:issn 0040-5779
    88 2305-3135
    89 schema:name Theoretical and Mathematical Physics
    90 rdf:type schema:Periodical
    91 sg:person.012424526446.93 schema:affiliation https://www.grid.ac/institutes/grid.445971.a
    92 schema:familyName Basuev
    93 schema:givenName A. G.
    94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012424526446.93
    95 rdf:type schema:Person
    96 sg:pub.10.1007/bf01009436 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015161718
    97 https://doi.org/10.1007/bf01009436
    98 rdf:type schema:CreativeWork
    99 sg:pub.10.1007/bf01009748 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017102814
    100 https://doi.org/10.1007/bf01009748
    101 rdf:type schema:CreativeWork
    102 sg:pub.10.1007/bf01010444 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049418892
    103 https://doi.org/10.1007/bf01010444
    104 rdf:type schema:CreativeWork
    105 sg:pub.10.1007/bf01016860 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035327444
    106 https://doi.org/10.1007/bf01016860
    107 rdf:type schema:CreativeWork
    108 sg:pub.10.1007/bf01017040 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012762935
    109 https://doi.org/10.1007/bf01017040
    110 rdf:type schema:CreativeWork
    111 sg:pub.10.1007/bf01017924 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033570166
    112 https://doi.org/10.1007/bf01017924
    113 rdf:type schema:CreativeWork
    114 sg:pub.10.1007/bf01018227 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007254359
    115 https://doi.org/10.1007/bf01018227
    116 rdf:type schema:CreativeWork
    117 sg:pub.10.1007/bf01026500 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045447468
    118 https://doi.org/10.1007/bf01026500
    119 rdf:type schema:CreativeWork
    120 sg:pub.10.1007/bf01040127 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047807510
    121 https://doi.org/10.1007/bf01040127
    122 rdf:type schema:CreativeWork
    123 sg:pub.10.1007/bf01048183 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044165425
    124 https://doi.org/10.1007/bf01048183
    125 rdf:type schema:CreativeWork
    126 sg:pub.10.1007/bf01152284 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016213776
    127 https://doi.org/10.1007/bf01152284
    128 rdf:type schema:CreativeWork
    129 sg:pub.10.1007/bf01197448 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047011008
    130 https://doi.org/10.1007/bf01197448
    131 rdf:type schema:CreativeWork
    132 sg:pub.10.1007/bf01197743 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040695034
    133 https://doi.org/10.1007/bf01197743
    134 rdf:type schema:CreativeWork
    135 sg:pub.10.1007/bf01197744 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031854114
    136 https://doi.org/10.1007/bf01197744
    137 rdf:type schema:CreativeWork
    138 sg:pub.10.1007/bf01206148 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042008012
    139 https://doi.org/10.1007/bf01206148
    140 rdf:type schema:CreativeWork
    141 sg:pub.10.1007/bf01206157 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018998981
    142 https://doi.org/10.1007/bf01206157
    143 rdf:type schema:CreativeWork
    144 sg:pub.10.1007/bf01212295 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021254136
    145 https://doi.org/10.1007/bf01212295
    146 rdf:type schema:CreativeWork
    147 sg:pub.10.1007/bf01217679 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011394911
    148 https://doi.org/10.1007/bf01217679
    149 rdf:type schema:CreativeWork
    150 sg:pub.10.1007/bf01224133 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012609545
    151 https://doi.org/10.1007/bf01224133
    152 rdf:type schema:CreativeWork
    153 sg:pub.10.1007/bf01614092 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037382141
    154 https://doi.org/10.1007/bf01614092
    155 rdf:type schema:CreativeWork
    156 sg:pub.10.1007/bf01646608 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029746508
    157 https://doi.org/10.1007/bf01646608
    158 rdf:type schema:CreativeWork
    159 sg:pub.10.1007/bf01942696 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039238256
    160 https://doi.org/10.1007/bf01942696
    161 rdf:type schema:CreativeWork
    162 sg:pub.10.1007/bf02099735 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024189378
    163 https://doi.org/10.1007/bf02099735
    164 rdf:type schema:CreativeWork
    165 sg:pub.10.1007/bf02108338 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046653185
    166 https://doi.org/10.1007/bf02108338
    167 rdf:type schema:CreativeWork
    168 sg:pub.10.1007/bf02179794 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037124056
    169 https://doi.org/10.1007/bf02179794
    170 rdf:type schema:CreativeWork
    171 sg:pub.10.1007/bf02188570 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016177871
    172 https://doi.org/10.1007/bf02188570
    173 rdf:type schema:CreativeWork
    174 sg:pub.10.1007/s00023-002-8616-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002783367
    175 https://doi.org/10.1007/s00023-002-8616-7
    176 rdf:type schema:CreativeWork
    177 sg:pub.10.1007/s00023-003-0149-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045457993
    178 https://doi.org/10.1007/s00023-003-0149-1
    179 rdf:type schema:CreativeWork
    180 sg:pub.10.1007/s002200050203 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034537827
    181 https://doi.org/10.1007/s002200050203
    182 rdf:type schema:CreativeWork
    183 sg:pub.10.1007/s00440-003-0328-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025882267
    184 https://doi.org/10.1007/s00440-003-0328-5
    185 rdf:type schema:CreativeWork
    186 sg:pub.10.1023/a:1023249608957 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046727891
    187 https://doi.org/10.1023/a:1023249608957
    188 rdf:type schema:CreativeWork
    189 https://doi.org/10.1063/1.434402 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058012433
    190 rdf:type schema:CreativeWork
    191 https://doi.org/10.1103/physreve.66.056117 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027507418
    192 rdf:type schema:CreativeWork
    193 https://doi.org/10.1103/revmodphys.57.827 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060839079
    194 rdf:type schema:CreativeWork
    195 https://doi.org/10.1137/1117073 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062866541
    196 rdf:type schema:CreativeWork
    197 https://doi.org/10.1209/0295-5075/3/7/012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064230474
    198 rdf:type schema:CreativeWork
    199 https://doi.org/10.1214/154957806000000050 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019455710
    200 rdf:type schema:CreativeWork
    201 https://www.grid.ac/institutes/grid.445971.a schema:alternateName Saint-Petersburg State University of Technology and Design
    202 schema:name Saint-Petersburg State University of Technology and Design, St. Petersburg, Russia
    203 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...