How many phases nucleate in the bidimensional Potts model?

TL;DR

This study investigates the nucleation process in the two-dimensional q > 4-state Potts model after a shallow quench, revealing a logarithmic relationship between the number of nucleating phases and system size due to a scaling symmetry.

Contribution

It uncovers the finite size scaling behavior of phase nucleation in the 2D Potts model for intermediate q values, highlighting a novel logarithmic dependence.

Findings

Nucleation involves k phases, with k increasing logarithmically with system size.

System initially behaves as if quenched to the critical temperature.

Finite size effects are governed by an underlying scaling symmetry.

Abstract

We study the kinetics of the two-dimensional q > 4-state Potts model after a shallow quench slightly below the critical temperature and above the pseudo spinodal. We use numerical methods and we focus on intermediate values of q, 4 < q < 100. We show that, initially, the system evolves as if it were quenched to the critical temperature. The further decay from the metastable state occurs by nucleation of k out of the q possible phases. For a given quench temperature, k is a logarithmically increasing function of the system size. This unusual finite size dependence is a consequence of a scaling symmetry underlying the nucleation phenomenon for these parameters.