How many phases nucleate in the bidimensional Potts model?

Abstract

We study the kinetics of the two-dimensional q > 4-state Potts model after a shallow quench to a temperature slightly below the critical one 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 configurations exhibit correlations that are indistinguishable from the ones in equilibrium at T c(q) over longer and longer length scales as time elapses. The further decay from the metastable state occurs by nucleation of an average number k out of the q possible phases. For a given quench temperature, k is a logarithmically increasing function of the system size, bounded by q. This unusual finite size dependence is a consequence of a scaling property underlying the nucleation phenomenon for these parameters.