On Models with Uncountable Set of Spin Values on a Cayley Tree: Integral Equations View Full Text


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Article Info

DATE

2010-07-27

AUTHORS

Utkir A. Rozikov, Yusup Kh. Eshkobilov

ABSTRACT

We consider models with nearest-neighbor interactions and with the set [0, 1] of spin values, on a Cayley tree of order k ⩾ 1. We reduce the problem of describing the “splitting Gibbs measures” of the model to the description of the solutions of some nonlinear integral equation. For k = 1 we show that the integral equation has a unique solution. In case k ⩾ 2 some models (with the set [0, 1] of spin values) which have a unique splitting Gibbs measure are constructed. Also for the Potts model with uncountable set of spin values it is proven that there is unique splitting Gibbs measure. More... »

PAGES

275-286

References to SciGraph publications

  • 1982-12. First-order phase transitions in large entropy lattice models in COMMUNICATIONS IN 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
  • 2004. Polynomials in NONE
  • 2006-01-06. The Potts Model with Countable Set of Spin Values on a Cayley Tree in LETTERS IN MATHEMATICAL PHYSICS
  • 2004-01. A Hard-Core Model on a Cayley Tree: An Example of a Loss Network in QUEUEING SYSTEMS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11040-010-9079-6

    DOI

    http://dx.doi.org/10.1007/s11040-010-9079-6

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1032764230


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