Low-temperature universal dynamics of the bidimensional Potts model in the large q limit

TL;DR

This paper investigates the low-temperature dynamics of the 2D Potts model at large q, revealing a universal coarsening process with a q-independent crossover temperature and Arrhenius time scales.

Contribution

It provides a detailed analysis of the universal dynamics and identifies a q-independent crossover temperature in the large q limit of the 2D Potts model.

Findings

Existence of a q-independent crossover temperature (pseudo spinodal).

Coarsening dynamics follow an Arrhenius time scale for large q.

Dynamic scaling behavior is universal across different lattice geometries.

Abstract

We study the low temperature quench dynamics of the two-dimensional Potts model in the limit of large number of states, q >> 1. We identify a q-independent crossover temperature (the pseudo spinodal) below which no high-temperature metastability stops the curvature driven coarsening process. At short length scales, the latter is decorated by freezing for some lattice geometries, notably the square one. With simple analytic arguments we evaluate the relevant time-scale in the coarsening regime, which turns out to be of Arrhenius form and independent of q for large q. Once taken into account dynamic scaling is universal.