A remark on the notion of robust phase transitions

TL;DR

This paper discusses the nature of phase transitions in the high-q Potts model, illustrating an example of a non-robust phase transition as recently defined.

Contribution

It provides a specific example of a non-robust phase transition in the high-q Potts model, challenging previous assumptions about phase transition robustness.

Findings

High-q Potts model exhibits non-robust phase transition at transition temperature.

The example clarifies the concept of non-robust phase transitions.

Supports recent theoretical definitions of phase transition robustness.

Abstract

We point out that the high-q Potts model on a regular lattice at its transition temperature provides an example of a non-robust - in the sense recently proposed by Pemantle and Steif- phase transition.