Long term ordering kinetics of the two dimensional q-state Potts model

TL;DR

This paper investigates the long-term non-equilibrium dynamics of the two-dimensional q-state Potts model, revealing different dynamical regimes, metastable states, and glassy behavior depending on temperature and system size.

Contribution

It provides a detailed analysis of the relaxation processes, metastable states, and finite size effects in the q-state Potts model after a quench, highlighting new dynamical regimes for q>4.

Findings

Existence of multiple dynamical regimes for q>4.

Identification of metastable states causing domain growth interruption.

Observation of glassy states at very low temperatures.

Abstract

We studied the non-equilibrium dynamics of the q-state Potts model in the square lattice, after a quench to sub-critical temperatures. By means of a continuous time Monte Carlo algorithm (non-conserved order parameter dynamics) we analyzed the long term behavior of the energy and relaxation time for a wide range of quench temperatures and system sizes. For q>4 we found the existence of different dynamical regimes, according to quench temperature range. At low (but finite) temperatures and very long times the Lifshitz-Allen-Cahn domain growth behavior is interrupted with finite probability when the system stuck in highly symmetric non-equilibrium metastable states, which induce activation in the domain growth, in agreement with early predictions of Lifshitz [JETP 42, 1354 (1962)]. Moreover, if the temperature is very low, the system always gets stuck at short times in a highly disordered metastable states with finite life time, which have been recently identified as glassy states. The finite size scaling properties of the different relaxation times involved, as well as their temperature dependency are analyzed in detail.