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We review and propose the use of associated dynamical system to explore the phase transition phenomena in p-adic statistical mechanics setting, by means of the renormalization techniques. Main focus of the paper is the p-adic \(\lambda \) -model on the Cayley tree. We study generalized p-adic quasi-Gibbs measures for the \(\lambda \) -model. These measures associate recurrence equations that determine dynamical systems for the model. A main point is to verify and confirm that the indicated predictions from a dynamical system point of view are indeed true.

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P-Adic Dynamical Systems for p-Adic \(\lambda \) -Models on the Cayley Trees

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  • 发表日期：

    2025年

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  • Farrukh Mukhamedov,
  • Otabek Khakimov

摘要

We review and propose the use of associated dynamical system to explore the phase transition phenomena in p-adic statistical mechanics setting, by means of the renormalization techniques. Main focus of the paper is the p-adic \(\lambda \) -model on the Cayley tree. We study generalized p-adic quasi-Gibbs measures for the \(\lambda \) -model. These measures associate recurrence equations that determine dynamical systems for the model. A main point is to verify and confirm that the indicated predictions from a dynamical system point of view are indeed true.