Thermodynamic versus Topological Phase Transitions: Cusp in the Kert\'esz Line

TL;DR

This paper analyzes phase transitions in the Curie--Weiss Potts model, revealing a cusp in the Kertész line where topological and thermodynamic transitions diverge, with explicit equations and cluster analysis.

Contribution

It provides explicit equations for the thermodynamic transition line and the Kertész line, highlighting the cusp where topological and thermodynamic transitions separate for the first time.

Findings

Explicit thermodynamic transition line in the β-h plane.

Identification of the Kertész line and its cusp.

Demonstration of the divergence between topological and thermodynamic transitions.

Abstract

We present a study of phase transitions of the Curie--Weiss Potts model at (inverse) temperature $\beta$, in presence of an external field $h$. Both thermodynamic and topological aspects of these transitions are considered. For the first aspect we complement previous results and give an explicit equation of the thermodynamic transition line in the $\beta$--$h$ plane as well as the magnitude of the jump of the magnetization (for $q \geqslant 3)$. The signature of the latter aspect is characterized here by the presence or not of a giant component in the clusters of a Fortuin--Kasteleyn type representation of the model. We give the equation of the Kert\'esz line separating (in the $\beta$--$h$ plane) the two behaviours. As a result, we get that this line exhibits, as soon as $q \geqslant 3$, a very interesting cusp where it separates from the thermodynamic transition line.