Zero-Temperature Coarsening in the 2d Potts Model

TL;DR

This paper investigates the zero-temperature coarsening dynamics of the 2d kinetic q-state Potts model, revealing complex static states, trapping phenomena, and unusual energy evolution, challenging traditional phase-ordering theories.

Contribution

It introduces a continuum Ginzburg-Landau description for the Potts model's coarsening process, capturing complex patterns and static states not explained by existing theories.

Findings

Presence of multiple static states including ground, stripe, and blinker states.

Unusual energy drops and macroscopic reordering during evolution.

Continuum equations successfully reproduce complex cluster patterns.

Abstract

We study the fate of the 2d kinetic q-state Potts model after a sudden quench to zero temperature. Both ground states and complicated static states are reached with non-zero probabilities. These outcomes resemble those found in the quench of the 2d Ising model; however, the variety of static states in the q-state Potts model (with q>=3) is much richer than in the Ising model, where static states are either ground or stripe states. Another possibility is that the system gets trapped on a set of equal-energy blinker states where a subset of spins can flip ad infinitum; these states are similar to those found in the quench of the 3d Ising model. The evolution towards the final energy is also unusual---at long times, sudden and massive energy drops may occur that are accompanied by macroscopic reordering of the domain structure. This indeterminacy in the zero-temperature quench of the kinetic Potts model is at odds with basic predictions from the theory of phase-ordering kinetics. We also propose a continuum description of coarsening with more than two equivalent ground states. The resulting time-dependent Ginzburg-Landau equations reproduce the complex cluster patterns that arise in the quench of the kinetic Potts model.