Static and dynamical aspects of the metastable states of first order transition systems

TL;DR

This paper investigates the metastable states of the 2D Potts model through numerical methods, analyzing equilibrium and relaxation behaviors, finite size effects, and free energy landscapes.

Contribution

It introduces a detailed numerical analysis of metastable states, including free energy extremal points and size-dependent nucleation dynamics, in the 2D Potts model.

Findings

Equilibrium spinodal temperature approaches bistable temperature with system size.

Size dependence of nucleation dynamics aligns with theoretical predictions.

Finite size scaling of free energy landscape at bistable point is performed.

Abstract

We numerically study the metastable states of the 2d Potts model. Both of equilibrium and relaxation properties are investigated focusing on the finite size effect. The former is investigated by finding the free energy extremal point by the Wang-Landau sampling and the latter is done by observing the Metropolis dynamics after sudden heating. It is explicitly shown that with increasing system size the equilibrium spinodal temperature approaches the bistable temperature in a power-law and the size-dependence of the nucleation dynamics agrees with it. In addition, we perform finite size scaling of the free energy landscape at the bistable point.