Chaotic behavior of the $P$-adic Potts-Bethe mapping

TL;DR

This paper investigates the chaotic dynamics of the $p$-adic Potts-Bethe mapping, providing new insights into $p$-adic dynamical systems related to statistical models on Cayley trees.

Contribution

It introduces a rigorous analysis of chaos in the $p$-adic Potts-Bethe mapping, a novel contribution not previously established for real-number counterparts.

Findings

Chaotic behavior identified in the $p$-adic Potts-Bethe mapping.

Provides rigorous proofs of chaos in the $p$-adic setting.

Extends understanding of $p$-adic dynamical systems in statistical physics.

Abstract

In our previous investigations, we have developed the renormalization group method to $p$-adic models on Cayley trees, this method is closely related to the investigation of $p$-adic dynamical systems associated with a given model. In this paper, we study chaotic behavior of the Potts-Bethe mapping. We point out that a similar kind of result is not known in the case of real numbers (with rigorous proofs).