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arXiv · 2509.16362

p-adic dynamical systems for $p$-adic $\lambda$-models on the Cayley trees

Farrukh Mukhamedov·Otabek Khakimov
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Abstract

We review and propose to 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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Farrukh Mukhamedov, Otabek Khakimov. 2025-09-19. p-adic dynamical systems for $p$-adic $\lambda$-models on the Cayley trees. https://arxiv.org/abs/2509.16362

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