Four competing interactions for models with an uncountable set of spin values on a Cayley tree View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-06

AUTHORS

U. A. Rozikov, F. H. Haydarov

ABSTRACT

We consider models with four competing interactions (external field, nearest neighbor, second neighbor, and three neighbors) and an uncountable set [0, 1] of spin values on the Cayley tree of order two. We reduce the problem of describing the splitting Gibbs measures of the model to the problem of analyzing solutions of a nonlinear integral equation and study some particular cases for Ising and Potts models. We also show that periodic Gibbs measures for the given models either are translation invariant or have the period two. We present examples where periodic Gibbs measures with the period two are not unique. More... »

PAGES

910-923

References to SciGraph publications

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  • 2004-02. On Gibbs Measures of Models with Competing Ternary and Binary Interactions and Corresponding von Neumann Algebras in JOURNAL OF STATISTICAL PHYSICS
  • 2002-03. Exact Solution of the Ising Model on the Cayley Tree with Competing Ternary and Binary Interactions in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2009-02-10. On Ising Model with Four Competing Interactions on Cayley Tree in MATHEMATICAL PHYSICS, ANALYSIS AND GEOMETRY
  • 2006-01-06. The Potts Model with Countable Set of Spin Values on a Cayley Tree in LETTERS IN MATHEMATICAL PHYSICS
  • 2012-08-11. Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree in MATHEMATICAL PHYSICS, ANALYSIS AND GEOMETRY
  • 2015-02-21. A Classical WR Model with q Particle Types in JOURNAL OF STATISTICAL PHYSICS
  • 2012-05-17. Non-uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree in JOURNAL OF STATISTICAL PHYSICS
  • 2014-12-01. Phase Transition and Critical Values of a Nearest-Neighbor System with Uncountable Local State Space on Cayley Trees in MATHEMATICAL PHYSICS, ANALYSIS AND GEOMETRY
  • 2010-07-27. On Models with Uncountable Set of Spin Values on a Cayley Tree: Integral Equations in MATHEMATICAL PHYSICS, ANALYSIS AND GEOMETRY
  • 1975-12. Phase diagrams of classical lattice systems in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1995-04. On the purity of the limiting gibbs state for the Ising model on the Bethe lattice in JOURNAL OF STATISTICAL PHYSICS
  • 2016-01-12. Positive fixed points of quadratic operators and Gibbs measures in POSITIVITY
  • 1976-01. Phase diagrams of classical lattice systems continuation in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2004-01. A Hard-Core Model on a Cayley Tree: An Example of a Loss Network in QUEUEING SYSTEMS
  • 1997-07. Partition structures of the cayley tree and applications for describing periodic gibbs distributions in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1982-12. First-order phase transitions in large entropy lattice models in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1134/s0040577917060095

    DOI

    http://dx.doi.org/10.1134/s0040577917060095

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1090321667


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