Condensation and Metastability in the 2D Potts Model

TL;DR

This paper investigates the nature of first-order phase transitions in the 2D Potts model, revealing observable effects of essential singularities and metastability phenomena through theoretical adaptation and numerical analysis.

Contribution

It adapts the droplet model to the 2D Potts model for q>4, linking parameters to critical properties and analyzing metastability and singularities.

Findings

Observable effects of essential singularity in free energy.

Metastability domain shrinks to zero in thermodynamic limit.

Numerical data supports theoretical predictions.

Abstract

For the first order transition of the Ising model below $T_c$, Isakov has proven that the free energy possesses an essential singularity in the applied field. Such a singularity in the control parameter, anticipated by condensation theory, is believed to be a generic feature of first order transitions, but too weak to be observable. We study these issues for the temperature driven transition of the $q$ states 2D Potts model at $q>q_c=4$. Adapting the droplet model to this case, we relate its parameters to the critical properties at $q_c$ and confront the free energy to the many informations brought by previous works. The essential singularity predicted at the transition temperature leads to observable effects in numerical data. On a finite lattice, a metastability domain of temperatures is identified, which shrinks to zero in the thermodynamical limit. ~