English

Gradient Gibbs measures with periodic boundary laws of a generalized SOS model on a Cayley tree

Probability 2023-09-06 v1 Functional Analysis

Abstract

We consider Gradient Gibbs measures corresponding to a periodic boundary law for a generalized SOS model with spin values from a countable set, on Cayley trees. On the Cayley tree, detailed information on Gradient Gibbs measures for models of SOS type are given in \cite{3, 16,8,11} and we continue the works for the generalized SOS model. Namely, in this paper, the problem of finding Gradient Gibbs measures that correspond to periodic boundary laws is reduced to a functional equation and by solving the equation all Gradient Gibbs measures with 4 periodic boundary laws are found.

Keywords

Cite

@article{arxiv.2309.00867,
  title  = {Gradient Gibbs measures with periodic boundary laws of a generalized SOS model on a Cayley tree},
  author = {F. H. Haydarov and R. A. Ilyasova},
  journal= {arXiv preprint arXiv:2309.00867},
  year   = {2023}
}