Perfect simulation for the infinite random cluster model, Ising and Potts models at low or high temperature

TL;DR

This paper introduces a novel perfect simulation algorithm for the infinite Potts model applicable at extreme temperature regimes, including the transition phase, with implications for boundary condition effects.

Contribution

The authors develop a new algorithm enabling perfect simulation of the infinite Potts model at both low and high temperatures, including the transition phase.

Findings

Algorithm successfully simulates the model at extreme temperatures

Results apply to free and constant boundary conditions

Provides new insights into phase transition behaviors

Abstract

In this article we create a new algorithm for the perfect simulation of the infinite Potts model at a sufficiently small or at a sufficiently high temperature, in particular under the transition phase temperature. We study the model for free boundary conditions and we give some consequences for the constant boundary conditions.