Abstract

In the present paper we study \(G_2\)-periodic \(p\)-adic quasi Gibbs measures for \(p\)-adic Potts model on a Cayley tree of order two. In the case \(q=3\), we prove the occurrence of a phase transition and construct ART quasi Gibbs measures for \(p\)-adic Potts model on a Cayley tree of order \(k\geq3\).

中文翻译：

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关于 $$G_2$$ -$$p$$ 的周期性准吉布斯测度 - Cayley 树上的 Adic Potts 模型

摘要

在本文中，我们研究了\(G_2\) -周期性\(p\) -adic 准吉布斯测度，用于在二阶 Cayley 树上的\(p\) -adic Potts 模型。在\(q=3\)的情况下，我们证明了相变的发生，并在\(k\geq3\)阶 Cayley 树上为\(p\) -adic Potts 模型构建了 ART准吉布斯测度。