Dynamics of the 2d Potts model phase transition

TL;DR

This paper investigates the non-equilibrium dynamics of the 2D Potts model during phase transitions, focusing on hysteresis effects and finite volume estimators to understand how dynamics alter statistical properties.

Contribution

It introduces a method to analyze hysteresis in the 2D Potts model and explores how dynamics influence the statistical properties of configurations near phase transitions.

Findings

Hysteresis shapes are used to estimate physical observables.

Dynamics significantly alter the statistical properties of configurations.

Finite volume estimators help study the approach to the thermodynamic limit.

Abstract

The dynamics of 2d Potts models, which are temperature driven through the phase transition using updating procedures in the Glauber universality class, is investigated. We present calculations of the hysteresis for the (internal) energy and for Fortuin-Kasteleyn clusters. The shape of the hysteresis is used to define finite volume estimators of physical observables, which can be used to study the approach to the infinite volume limit. We compare with equilibrium configurations and the preliminary indications are that the dynamics leads to considerable alterations of the statistical properties of the configurations studied.