Phenomenological theory of the Potts model evaporation-condensation transition

TL;DR

This paper develops a phenomenological theory for the finite-size evaporation-condensation transition in the q-state Potts model, linking the transition behavior to a surface-volume exponent and validating it with large-scale simulations.

Contribution

It introduces a new theoretical framework connecting the transition properties to an exponent relating droplet surface and volume, supported by extensive simulations.

Findings

Transition temperature and energy converge with system size as predicted.

The exponent a is compatible with 1/4 for the 2D Potts model.

The surface-volume exponent σ is estimated as 2/3, aligning with previous theories.

Abstract

We present a phenomenological theory describing the finite-size evaporation-condensation transition of the $q$-state Potts model in the microcanonical ensemble. Our arguments rely on the existence of an exponent $\sigma$, relating the surface and the volume of the condensed phase droplet. The evaporation-condensation transition temperature and energy converge to their infinite-size values with the same power, $a=(1-\sigma)/(2-\sigma)$, of the inverse of the system size. For the 2D Potts model we show, by means of efficient simulations up to $q=24$ and $1024^2$ sites, that the exponent $a$ is compatible with $1/4$, in disagreement with previous studies. While this value cannot be addressed by the evaporation-condensation theory developed for the Ising model, it is obtained in the present scheme if $\sigma=2/3$, in agreement with previous theoretical guesses. The connection with the phenomenon of metastability in the canonical ensemble is also discussed.