Title: On phase transitions of the Potts model with three competing interactions on Cayley tree
Author(s):

	H. Akin (Department of Mathematics, Faculty of Education, Zirve University, 27260 Gaziantep, Turkey ) ,
	S. Temir (Department of Mathematics, Arts and Science Faculty Harran University, 63200 Sanliurfa, Turkey)

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.

Key words: phase transition, Potts model, competing interactions, Gibbs measure
PACS: 05.50.+q, 64.60.-i, 64.60.De, 75.10.Hk

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