Cayley树上三相互作用Potts模型的相变
On phase transitions of the Potts model with three competing interactions on Cayley tree
摘要：
本文研究了二阶Cayley树上具有最近邻、次邻和三重邻相互作用的Potts模型在非零外场作用下的相变问题。我们证明了对于模型的某些参数值，存在相变。我们把限制吉布斯测度的描述问题归结为求解非线性函数方程的问题。我们推广了Ganikhodjaev和Rozikov [Math.Phys.Anal. Geom.，2009，12，No. 2，141-156]关于Ising模型到Potts模型设置的相变。
英文摘要：
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.
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