Phase Transition in Subshifts of Finite Type via Hofbauer Potential

TL;DR

This paper investigates phase transitions in the pressure function of subshifts of finite type using the Hofbauer potential, showing a freezing transition where the measure concentrates on the subshift and the pressure function becomes smooth at the transition point.

Contribution

It establishes the occurrence of freezing phase transitions in the pressure function related to the Hofbauer potential and characterizes the smoothness at the transition point.

Findings

Pressure function exhibits freezing phase transition.

Post-transition measure concentrates on the subshift.

Pressure function is C1-smooth at the transition.

Abstract

The aim of this article is to establish freezing phase transition of the pressure function, considering the generalized Hofbauer potential {\phi}, which is connected to the distance from subshift of finite type {\Sigma}F in the full shift {\Sigma} over finite alphabets. Our objective is to prove that the pressure function exhibits phase transition with the dominating measure is highly concentrated on {\Sigma}F after the transition. Moreover, the pressure function attains C1-smoothness when the transition occurs at 2.