Large deviation principle of Multiplicative Ising models on Markov-Cayley Trees

Jung-Chao Ban; Wen-Guei Hu; Zongfan Zhang

Large deviation principle of Multiplicative Ising models on Markov-Cayley Trees

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arxiv 2305.08630 v1 pith:55RSFNF5 submitted 2023-05-15 math.DS math.PR

Jung-Chao Ban , Wen-Guei Hu , Zongfan Zhang This is my paper · ORCID

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keywords functionsdeviationenergyfreeisinglargemodelsmultiplicative

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In this paper, we study the large deviation principle (LDP) for two types (Type I and Type II) of multiplicative Ising models. For Types I and II, the explicit formulas for the free energy functions and the associated rate functions are derived. Furthermore, we prove that those free energy functions are differentiable, which indicates that both systems are characterized by a lack of phase transition phenomena.

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