Non-uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2012-05-17

AUTHORS

Y. K. Eshkabilov, F. H. Haydarov, U. A. Rozikov

ABSTRACT

In this paper we construct several models with nearest-neighbor interactions and with the set [0,1] of spin values, on a Cayley tree of order k≥2. We prove that each of the constructed model has at least two translational-invariant Gibbs measures.

PAGES

779-794

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10955-012-0494-x

DOI

http://dx.doi.org/10.1007/s10955-012-0494-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1033373089


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": "National University of Uzbekistan, Tashkent, Uzbekistan", 
          "id": "http://www.grid.ac/institutes/grid.23471.33", 
          "name": [
            "National University of Uzbekistan, Tashkent, Uzbekistan"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Eshkabilov", 
        "givenName": "Y. K.", 
        "id": "sg:person.015547714741.65", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015547714741.65"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "National University of Uzbekistan, Tashkent, Uzbekistan", 
          "id": "http://www.grid.ac/institutes/grid.23471.33", 
          "name": [
            "National University of Uzbekistan, Tashkent, Uzbekistan"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Haydarov", 
        "givenName": "F. H.", 
        "id": "sg:person.015457756641.48", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015457756641.48"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institute of Mathematics, Tashkent, Uzbekistan", 
          "id": "http://www.grid.ac/institutes/None", 
          "name": [
            "Institute of Mathematics, 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"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s11040-009-9056-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032320792", 
          "https://doi.org/10.1007/s11040-009-9056-0"
        ], 
        "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"
      }, 
      {
        "id": "sg:pub.10.1007/bf02634202", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042152983", 
          "https://doi.org/10.1007/bf02634202"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02179399", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029115716", 
          "https://doi.org/10.1007/bf02179399"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/b:ques.0000021149.43343.05", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014082630", 
          "https://doi.org/10.1023/b:ques.0000021149.43343.05"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11040-010-9079-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032764230", 
          "https://doi.org/10.1007/s11040-010-9079-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02634109", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000760297", 
          "https://doi.org/10.1007/bf02634109"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2012-05-17", 
    "datePublishedReg": "2012-05-17", 
    "description": "In this paper we construct several models with nearest-neighbor interactions and with the set [0,1] of spin values, on a Cayley tree of order k\u22652. We prove that each of the constructed model has at least two translational-invariant Gibbs measures.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s10955-012-0494-x", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1040979", 
        "issn": [
          "0022-4715", 
          "1572-9613"
        ], 
        "name": "Journal of Statistical Physics", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "4", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "147"
      }
    ], 
    "keywords": [
      "Gibbs measures", 
      "Cayley tree", 
      "uncountable set", 
      "nearest-neighbor interactions", 
      "model", 
      "set", 
      "spin values", 
      "trees", 
      "measures", 
      "values", 
      "order", 
      "interaction", 
      "paper", 
      "translational-invariant Gibbs measures"
    ], 
    "name": "Non-uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree", 
    "pagination": "779-794", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1033373089"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10955-012-0494-x"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10955-012-0494-x", 
      "https://app.dimensions.ai/details/publication/pub.1033373089"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2021-11-01T18:18", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20211101/entities/gbq_results/article/article_566.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s10955-012-0494-x"
  }
]
 

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/s10955-012-0494-x'

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/s10955-012-0494-x'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10955-012-0494-x'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10955-012-0494-x'


 

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

117 TRIPLES      22 PREDICATES      46 URIs      31 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10955-012-0494-x schema:about anzsrc-for:01
2 anzsrc-for:02
3 schema:author N8ee4392ea0fa4216b2989b9a71a915d9
4 schema:citation sg:pub.10.1007/bf02179399
5 sg:pub.10.1007/bf02634109
6 sg:pub.10.1007/bf02634202
7 sg:pub.10.1007/s11005-005-0032-8
8 sg:pub.10.1007/s11040-009-9056-0
9 sg:pub.10.1007/s11040-010-9079-6
10 sg:pub.10.1023/b:ques.0000021149.43343.05
11 schema:datePublished 2012-05-17
12 schema:datePublishedReg 2012-05-17
13 schema:description In this paper we construct several models with nearest-neighbor interactions and with the set [0,1] of spin values, on a Cayley tree of order k≥2. We prove that each of the constructed model has at least two translational-invariant Gibbs measures.
14 schema:genre article
15 schema:inLanguage en
16 schema:isAccessibleForFree true
17 schema:isPartOf N0fd7250ce77a41b191dec0ad9943b45f
18 N5420189a6632434db732e270e4287144
19 sg:journal.1040979
20 schema:keywords Cayley tree
21 Gibbs measures
22 interaction
23 measures
24 model
25 nearest-neighbor interactions
26 order
27 paper
28 set
29 spin values
30 translational-invariant Gibbs measures
31 trees
32 uncountable set
33 values
34 schema:name Non-uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree
35 schema:pagination 779-794
36 schema:productId N17bf949fde214f74a25f9184f7144a8e
37 Na9e964008db94c0f906209c655d94168
38 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033373089
39 https://doi.org/10.1007/s10955-012-0494-x
40 schema:sdDatePublished 2021-11-01T18:18
41 schema:sdLicense https://scigraph.springernature.com/explorer/license/
42 schema:sdPublisher N335cbf5ec07d4f2b9f38a7951349e8a9
43 schema:url https://doi.org/10.1007/s10955-012-0494-x
44 sgo:license sg:explorer/license/
45 sgo:sdDataset articles
46 rdf:type schema:ScholarlyArticle
47 N0fd7250ce77a41b191dec0ad9943b45f schema:issueNumber 4
48 rdf:type schema:PublicationIssue
49 N17bf949fde214f74a25f9184f7144a8e schema:name dimensions_id
50 schema:value pub.1033373089
51 rdf:type schema:PropertyValue
52 N2bf845f447c8403fb98f6ce01b5aa63a rdf:first sg:person.015457756641.48
53 rdf:rest Ncb4e6ffc033d4fe4b4f05f55a75019fd
54 N335cbf5ec07d4f2b9f38a7951349e8a9 schema:name Springer Nature - SN SciGraph project
55 rdf:type schema:Organization
56 N5420189a6632434db732e270e4287144 schema:volumeNumber 147
57 rdf:type schema:PublicationVolume
58 N8ee4392ea0fa4216b2989b9a71a915d9 rdf:first sg:person.015547714741.65
59 rdf:rest N2bf845f447c8403fb98f6ce01b5aa63a
60 Na9e964008db94c0f906209c655d94168 schema:name doi
61 schema:value 10.1007/s10955-012-0494-x
62 rdf:type schema:PropertyValue
63 Ncb4e6ffc033d4fe4b4f05f55a75019fd rdf:first sg:person.014213263324.92
64 rdf:rest rdf:nil
65 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
66 schema:name Mathematical Sciences
67 rdf:type schema:DefinedTerm
68 anzsrc-for:02 schema:inDefinedTermSet anzsrc-for:
69 schema:name Physical Sciences
70 rdf:type schema:DefinedTerm
71 sg:journal.1040979 schema:issn 0022-4715
72 1572-9613
73 schema:name Journal of Statistical Physics
74 schema:publisher Springer Nature
75 rdf:type schema:Periodical
76 sg:person.014213263324.92 schema:affiliation grid-institutes:None
77 schema:familyName Rozikov
78 schema:givenName U. A.
79 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014213263324.92
80 rdf:type schema:Person
81 sg:person.015457756641.48 schema:affiliation grid-institutes:grid.23471.33
82 schema:familyName Haydarov
83 schema:givenName F. H.
84 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015457756641.48
85 rdf:type schema:Person
86 sg:person.015547714741.65 schema:affiliation grid-institutes:grid.23471.33
87 schema:familyName Eshkabilov
88 schema:givenName Y. K.
89 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015547714741.65
90 rdf:type schema:Person
91 sg:pub.10.1007/bf02179399 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029115716
92 https://doi.org/10.1007/bf02179399
93 rdf:type schema:CreativeWork
94 sg:pub.10.1007/bf02634109 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000760297
95 https://doi.org/10.1007/bf02634109
96 rdf:type schema:CreativeWork
97 sg:pub.10.1007/bf02634202 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042152983
98 https://doi.org/10.1007/bf02634202
99 rdf:type schema:CreativeWork
100 sg:pub.10.1007/s11005-005-0032-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038943181
101 https://doi.org/10.1007/s11005-005-0032-8
102 rdf:type schema:CreativeWork
103 sg:pub.10.1007/s11040-009-9056-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032320792
104 https://doi.org/10.1007/s11040-009-9056-0
105 rdf:type schema:CreativeWork
106 sg:pub.10.1007/s11040-010-9079-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032764230
107 https://doi.org/10.1007/s11040-010-9079-6
108 rdf:type schema:CreativeWork
109 sg:pub.10.1023/b:ques.0000021149.43343.05 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014082630
110 https://doi.org/10.1023/b:ques.0000021149.43343.05
111 rdf:type schema:CreativeWork
112 grid-institutes:None schema:alternateName Institute of Mathematics, Tashkent, Uzbekistan
113 schema:name Institute of Mathematics, Tashkent, Uzbekistan
114 rdf:type schema:Organization
115 grid-institutes:grid.23471.33 schema:alternateName National University of Uzbekistan, Tashkent, Uzbekistan
116 schema:name National University of Uzbekistan, Tashkent, Uzbekistan
117 rdf:type schema:Organization
 




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


...