Phase separation of the Potts model in que square lattice

TL;DR

This paper investigates the phase separation dynamics of the two-dimensional q-state Potts model on a square lattice, focusing on zero and finite temperature behaviors, and how they depend on the number of states q.

Contribution

It provides numerical insights into the ordering process and energy evolution of the Potts model at different temperatures, highlighting the effects of q on phase separation.

Findings

Energy decreases follow Allen-Cahn law at zero temperature.

System converges to higher-energy states for q>4.

Finite temperature delays ordering and domain growth slows as q increases.

Abstract

When the two dimensional q-color Potts model in the square lattice is quenched at zero temperature with Glauber dynamics, the energy decreases in time following an Allen-Cahn power law, and the system converges to a phase with energy higher than the ground state energy after an arbitrary large time when q>4. At low but finite temperature, it cesses to obey the power-law regime and orders after a very long time, which increases with q, and before which it performs a domain growth process which tends to be slower as q increases. We briefly present and comment numerical results on the ordering at nonzero temperature.