Gibbs measures for the HC Blume–Capel model with countably many states on a Cayley tree View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2022-06-23

AUTHORS

N. N. Ganikhodzhaev, U. A. Rozikov, N. M. Khatamov

ABSTRACT

We study the Blume–Capel model with a countable set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb Z$$\end{document} of spin values and a force \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J\in \mathbb R$$\end{document} of interaction between the nearest neighbors on a Cayley tree of order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\geq 2$$\end{document}. The following results are obtained. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta=e^{-J/T}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T>0$$\end{document}, be the temperature. For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta\geq 1$$\end{document}, there exist no translation invariant Gibbs measures or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}-periodic Gibbs measures. For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<\theta< 1$$\end{document}, we prove the uniqueness of a translation-invariant Gibbs measure. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta=\sum_i\theta^{(k+1)i^2}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta_\mathrm{cr}(k)=k^k/(k-1)^{k+1}$$\end{document}. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<\Theta\leq\Theta_\mathrm{cr}$$\end{document}, then there exists exactly one \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}-periodic Gibbs measure that is translation invariant. For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta>\Theta_\mathrm{cr}$$\end{document}, there exist exactly three \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}-periodic Gibbs measures, one of which is a translation-invariant Gibbs measure. More... »

PAGES

856-865

References to SciGraph publications

  • 1991-07. Random surfaces with two-sided constraints: An application of the theory of dominant ground states in JOURNAL OF STATISTICAL PHYSICS
  • 2021-02-06. Phase transitions for a class of gradient fields in PROBABILITY THEORY AND RELATED FIELDS
  • 1996-05. Metastability and nucleation for the Blume-Capel model. Different mechanisms of transition in JOURNAL OF STATISTICAL PHYSICS
  • 2021-03. Holliday junctions in the Blume–Capel model of DNA in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2006-01-06. The Potts Model with Countable Set of Spin Values on a Cayley Tree in LETTERS IN MATHEMATICAL PHYSICS
  • 2020-09. Translation-Invariant Extreme Gibbs Measures for the Blume–Capel Model Withwand on a Cayley Tree in UKRAINIAN MATHEMATICAL JOURNAL
  • 2020-08-13. Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2021-09-13. Metastability of Blume–Capel Model with Zero Chemical Potential and Zero External Field in JOURNAL OF STATISTICAL PHYSICS
  • <error retrieving object. in <ERROR RETRIEVING OBJECT
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1134/s0040577922060071

    DOI

    http://dx.doi.org/10.1134/s0040577922060071

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1148913273


    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/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/02", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Physical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan", 
              "id": "http://www.grid.ac/institutes/grid.419209.7", 
              "name": [
                "Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Ganikhodzhaev", 
            "givenName": "N. N.", 
            "id": "sg:person.010650336574.13", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010650336574.13"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan", 
              "id": "http://www.grid.ac/institutes/grid.23471.33", 
              "name": [
                "Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan", 
                "AKFA University, Tashkent, Uzbekistan", 
                "Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Rozikov", 
            "givenName": "U. A.", 
            "id": "sg:person.014213263324.92", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014213263324.92"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Namangan State University, Namangan, Uzbekistan", 
              "id": "http://www.grid.ac/institutes/grid.444646.0", 
              "name": [
                "Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan", 
                "Namangan State University, Namangan, Uzbekistan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Khatamov", 
            "givenName": "N. M.", 
            "id": "sg:person.012216724546.03", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012216724546.03"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf02183739", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047938539", 
              "https://doi.org/10.1007/bf02183739"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01057870", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000126993", 
              "https://doi.org/10.1007/bf01057870"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1134/s0040577921030090", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1139032409", 
              "https://doi.org/10.1134/s0040577921030090"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4757-2539-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038602576", 
              "https://doi.org/10.1007/978-1-4757-2539-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1134/s0040577920080073", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1130312695", 
              "https://doi.org/10.1134/s0040577920080073"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10955-021-02823-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1141079365", 
              "https://doi.org/10.1007/s10955-021-02823-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11253-020-01804-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1131885691", 
              "https://doi.org/10.1007/s11253-020-01804-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00440-020-01021-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1135184370", 
              "https://doi.org/10.1007/s00440-020-01021-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11005-005-0032-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038943181", 
              "https://doi.org/10.1007/s11005-005-0032-8"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2022-06-23", 
        "datePublishedReg": "2022-06-23", 
        "description": "Abstract  We study the Blume\u2013Capel model with a countable set \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathbb Z$$\\end{document} of  spin values and a force \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J\\in \\mathbb R$$\\end{document} of interaction between the  nearest neighbors on a Cayley tree of order \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$k\\geq 2$$\\end{document}. The following  results are obtained. Let \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\theta=e^{-J/T}$$\\end{document}, \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$T>0$$\\end{document}, be the  temperature. For \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\theta\\geq 1$$\\end{document}, there exist no translation  invariant Gibbs measures or \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2$$\\end{document}-periodic Gibbs measures. For  \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0<\\theta< 1$$\\end{document}, we prove the uniqueness of a translation-invariant Gibbs measure. Let  \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Theta=\\sum_i\\theta^{(k+1)i^2}$$\\end{document} and  \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Theta_\\mathrm{cr}(k)=k^k/(k-1)^{k+1}$$\\end{document}. If  \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0<\\Theta\\leq\\Theta_\\mathrm{cr}$$\\end{document}, then there exists exactly one  \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2$$\\end{document}-periodic Gibbs measure that is translation invariant. For  \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Theta>\\Theta_\\mathrm{cr}$$\\end{document}, there exist exactly three \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2$$\\end{document}-periodic  Gibbs measures, one of which is a translation-invariant Gibbs  measure.", 
        "genre": "article", 
        "id": "sg:pub.10.1134/s0040577922060071", 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1327888", 
            "issn": [
              "0040-5779", 
              "1573-9333"
            ], 
            "name": "Theoretical and Mathematical Physics", 
            "publisher": "Pleiades Publishing", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "211"
          }
        ], 
        "keywords": [
          "Blume-Capel model", 
          "Cayley tree", 
          "invariant Gibbs measures", 
          "Gibbs measures", 
          "model", 
          "countable set", 
          "set", 
          "spin values", 
          "values", 
          "force", 
          "interaction", 
          "nearest neighbors", 
          "neighbors", 
          "trees", 
          "order", 
          "results", 
          "temperature", 
          "translation", 
          "measures", 
          "periodic Gibbs measures", 
          "uniqueness", 
          "translation-invariant Gibbs measures", 
          "translation invariant", 
          "invariants", 
          "Gibbs", 
          "state"
        ], 
        "name": "Gibbs measures for the HC Blume\u2013Capel model with countably many states on a Cayley tree", 
        "pagination": "856-865", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1148913273"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1134/s0040577922060071"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1134/s0040577922060071", 
          "https://app.dimensions.ai/details/publication/pub.1148913273"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-10-01T06:51", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20221001/entities/gbq_results/article/article_948.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1134/s0040577922060071"
      }
    ]
     

    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.10.1134/s0040577922060071'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1134/s0040577922060071'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1134/s0040577922060071'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1134/s0040577922060071'


     

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

    142 TRIPLES      21 PREDICATES      59 URIs      42 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1134/s0040577922060071 schema:about anzsrc-for:01
    2 anzsrc-for:02
    3 schema:author N9b0712fd419740ea97e307fc6b2046aa
    4 schema:citation sg:pub.10.1007/978-1-4757-2539-1
    5 sg:pub.10.1007/bf01057870
    6 sg:pub.10.1007/bf02183739
    7 sg:pub.10.1007/s00440-020-01021-5
    8 sg:pub.10.1007/s10955-021-02823-0
    9 sg:pub.10.1007/s11005-005-0032-8
    10 sg:pub.10.1007/s11253-020-01804-y
    11 sg:pub.10.1134/s0040577920080073
    12 sg:pub.10.1134/s0040577921030090
    13 schema:datePublished 2022-06-23
    14 schema:datePublishedReg 2022-06-23
    15 schema:description Abstract We study the Blume–Capel model with a countable set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb Z$$\end{document} of spin values and a force \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J\in \mathbb R$$\end{document} of interaction between the nearest neighbors on a Cayley tree of order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\geq 2$$\end{document}. The following results are obtained. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta=e^{-J/T}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T>0$$\end{document}, be the temperature. For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta\geq 1$$\end{document}, there exist no translation invariant Gibbs measures or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}-periodic Gibbs measures. For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<\theta< 1$$\end{document}, we prove the uniqueness of a translation-invariant Gibbs measure. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta=\sum_i\theta^{(k+1)i^2}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta_\mathrm{cr}(k)=k^k/(k-1)^{k+1}$$\end{document}. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<\Theta\leq\Theta_\mathrm{cr}$$\end{document}, then there exists exactly one \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}-periodic Gibbs measure that is translation invariant. For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta>\Theta_\mathrm{cr}$$\end{document}, there exist exactly three \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}-periodic Gibbs measures, one of which is a translation-invariant Gibbs measure.
    16 schema:genre article
    17 schema:isAccessibleForFree false
    18 schema:isPartOf N3ecc095b8ec54a2b98e1af4300cc9175
    19 N6492b8c432604f85ba4da421e5b5cd90
    20 sg:journal.1327888
    21 schema:keywords Blume-Capel model
    22 Cayley tree
    23 Gibbs
    24 Gibbs measures
    25 countable set
    26 force
    27 interaction
    28 invariant Gibbs measures
    29 invariants
    30 measures
    31 model
    32 nearest neighbors
    33 neighbors
    34 order
    35 periodic Gibbs measures
    36 results
    37 set
    38 spin values
    39 state
    40 temperature
    41 translation
    42 translation invariant
    43 translation-invariant Gibbs measures
    44 trees
    45 uniqueness
    46 values
    47 schema:name Gibbs measures for the HC Blume–Capel model with countably many states on a Cayley tree
    48 schema:pagination 856-865
    49 schema:productId N31879195c19c49c28ea8242a3ba24a97
    50 N3cbc8b7e7149403bbf2b05a073137a84
    51 schema:sameAs https://app.dimensions.ai/details/publication/pub.1148913273
    52 https://doi.org/10.1134/s0040577922060071
    53 schema:sdDatePublished 2022-10-01T06:51
    54 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    55 schema:sdPublisher Ndf932536de4048ceabcb57fbe9d3e477
    56 schema:url https://doi.org/10.1134/s0040577922060071
    57 sgo:license sg:explorer/license/
    58 sgo:sdDataset articles
    59 rdf:type schema:ScholarlyArticle
    60 N31879195c19c49c28ea8242a3ba24a97 schema:name dimensions_id
    61 schema:value pub.1148913273
    62 rdf:type schema:PropertyValue
    63 N3cbc8b7e7149403bbf2b05a073137a84 schema:name doi
    64 schema:value 10.1134/s0040577922060071
    65 rdf:type schema:PropertyValue
    66 N3ecc095b8ec54a2b98e1af4300cc9175 schema:issueNumber 3
    67 rdf:type schema:PublicationIssue
    68 N6492b8c432604f85ba4da421e5b5cd90 schema:volumeNumber 211
    69 rdf:type schema:PublicationVolume
    70 N9b0712fd419740ea97e307fc6b2046aa rdf:first sg:person.010650336574.13
    71 rdf:rest Nfbc1f101927648aab6e73341fe9b5bd3
    72 Nafa8dc84d50d4237ae0cd9da45cf945a rdf:first sg:person.012216724546.03
    73 rdf:rest rdf:nil
    74 Ndf932536de4048ceabcb57fbe9d3e477 schema:name Springer Nature - SN SciGraph project
    75 rdf:type schema:Organization
    76 Nfbc1f101927648aab6e73341fe9b5bd3 rdf:first sg:person.014213263324.92
    77 rdf:rest Nafa8dc84d50d4237ae0cd9da45cf945a
    78 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    79 schema:name Mathematical Sciences
    80 rdf:type schema:DefinedTerm
    81 anzsrc-for:02 schema:inDefinedTermSet anzsrc-for:
    82 schema:name Physical Sciences
    83 rdf:type schema:DefinedTerm
    84 sg:journal.1327888 schema:issn 0040-5779
    85 1573-9333
    86 schema:name Theoretical and Mathematical Physics
    87 schema:publisher Pleiades Publishing
    88 rdf:type schema:Periodical
    89 sg:person.010650336574.13 schema:affiliation grid-institutes:grid.419209.7
    90 schema:familyName Ganikhodzhaev
    91 schema:givenName N. N.
    92 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010650336574.13
    93 rdf:type schema:Person
    94 sg:person.012216724546.03 schema:affiliation grid-institutes:grid.444646.0
    95 schema:familyName Khatamov
    96 schema:givenName N. M.
    97 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012216724546.03
    98 rdf:type schema:Person
    99 sg:person.014213263324.92 schema:affiliation grid-institutes:grid.23471.33
    100 schema:familyName Rozikov
    101 schema:givenName U. A.
    102 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014213263324.92
    103 rdf:type schema:Person
    104 sg:pub.10.1007/978-1-4757-2539-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038602576
    105 https://doi.org/10.1007/978-1-4757-2539-1
    106 rdf:type schema:CreativeWork
    107 sg:pub.10.1007/bf01057870 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000126993
    108 https://doi.org/10.1007/bf01057870
    109 rdf:type schema:CreativeWork
    110 sg:pub.10.1007/bf02183739 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047938539
    111 https://doi.org/10.1007/bf02183739
    112 rdf:type schema:CreativeWork
    113 sg:pub.10.1007/s00440-020-01021-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1135184370
    114 https://doi.org/10.1007/s00440-020-01021-5
    115 rdf:type schema:CreativeWork
    116 sg:pub.10.1007/s10955-021-02823-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1141079365
    117 https://doi.org/10.1007/s10955-021-02823-0
    118 rdf:type schema:CreativeWork
    119 sg:pub.10.1007/s11005-005-0032-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038943181
    120 https://doi.org/10.1007/s11005-005-0032-8
    121 rdf:type schema:CreativeWork
    122 sg:pub.10.1007/s11253-020-01804-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1131885691
    123 https://doi.org/10.1007/s11253-020-01804-y
    124 rdf:type schema:CreativeWork
    125 sg:pub.10.1134/s0040577920080073 schema:sameAs https://app.dimensions.ai/details/publication/pub.1130312695
    126 https://doi.org/10.1134/s0040577920080073
    127 rdf:type schema:CreativeWork
    128 sg:pub.10.1134/s0040577921030090 schema:sameAs https://app.dimensions.ai/details/publication/pub.1139032409
    129 https://doi.org/10.1134/s0040577921030090
    130 rdf:type schema:CreativeWork
    131 grid-institutes:grid.23471.33 schema:alternateName Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan
    132 schema:name AKFA University, Tashkent, Uzbekistan
    133 Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan
    134 Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan
    135 rdf:type schema:Organization
    136 grid-institutes:grid.419209.7 schema:alternateName Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan
    137 schema:name Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan
    138 rdf:type schema:Organization
    139 grid-institutes:grid.444646.0 schema:alternateName Namangan State University, Namangan, Uzbekistan
    140 schema:name Namangan State University, Namangan, Uzbekistan
    141 Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan
    142 rdf:type schema:Organization
     




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


    ...