Deformations of Dynamics Associated to the Chiral Potts Model

TL;DR

This paper explores deformations of birational group representations linked to the five-state Potts model, revealing exact analogies at Fermat numbers and analyzing the stability of these dynamics, especially finite orbits.

Contribution

It introduces a novel deformation framework for group representations related to the chiral Potts model, connecting it to Fermat numbers and stability analysis.

Findings

Deformation parameters relate to the number of states in the Potts model.

Exact analogy at Fermat numbers for the deformation parameter.

Stability analysis of finite order orbits in the deformed dynamics.

Abstract

We describe deformations of non-linear (birational) representations of discrete groups generated by involutions, having their origin in the theory of the symmetric five-state Potts model. One of the deformation parameters can be seen as the number $q$ of states of a chiral Potts models. This analogy becomes exact when $q$ is a Fermat number. We analyze the stability of the corresponding dynamics, with a particular attention to orbits of finite order.