On phase transitions of the Potts model with three competing interactions on Cayley tree

Abstract

In the present paper we study a phase transition problem for the Potts model with three competing interactions, the nearest neighbors, the second neighbors and triples of neighbors and non-zero external field on Cayley tree of order two. We prove that for some parameter values of the model there is phase transition. We reduce the problem of describing by limiting Gibbs measures to the problem of solving a system of nonlinear functional equations. We extend the results obtained by Ganikhodjaev and Rozikov [Math. Phys. Anal. Geom., 2009, 12, No. 2, 141-156] on phase transition for the Ising model to the Potts model setting.

11 pages, 3 figures. Published version with title changed

References in corpus (1)

• On Gibbs Measures of Models with Competing Ternary and Binary Interactions and Corresponding Von Neumann Algebras II

Cited by in corpus (4)

• Using New Approaches to obtain Gibbs Measures of Vannimenus model on a Cayley tree
• Phase transition and Gibbs Measures of Vannimenus model on semi-infinite Cayley tree of order three
• Gibbs measures of an Ising model with competing interactions on the triangular chandelier-lattice
• Determination of paramagnetic and ferromagnetic phases of an Ising model on a third-order Cayley tree