Thermodynamic versus Topological Phase Transitions: Cusp in the Kertész Line

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 $q⩾3)$. 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 Kertész line separating (in the $\beta$--$h$ plane) the two behaviours. As a result, we get that this line exhibits, as soon as $q⩾3$, a very interesting cusp where it separates from the thermodynamic transition line.

References in corpus (5)

• The Random-Cluster Model
• Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model
• Mean-field driven first-order phase transitions in systems with long-range interactions
• Large-deviations/thermodynamic approach to percolation on the complete graph
• On the Kertész line: Thermodynamic versus Geometric Criticality

Cited by in corpus (3)

• Limit Theorems and Coexistence Probabilities for the Curie-Weiss Potts Model with an external field
• Yang-Lee zeros and the critical behavior of the infinite-range two- and three-state Potts models
• Statistics of geometric clusters in Potts model: statistical mechanics approach