Freezing vs. equilibration dynamics in the Potts model

TL;DR

This paper investigates the dynamics of the q-Potts model after sudden temperature quenches, revealing how lattice topology influences whether the system freezes or reaches equilibrium, especially in the large-q limit.

Contribution

It identifies the role of lattice structure, cyclic versus acyclic, in determining the freezing or equilibration of the q-Potts model dynamics at large q.

Findings

Acyclic lattice structures cause dynamical freezing.

Cyclic lattice structures facilitate reaching equilibrium.

Lattice topology, not coordination number, governs dynamics.

Abstract

We study the quench dynamics of the $q$ Potts model on different bi/tri-dimensional lattice topologies. In particular we are interested in instantaneous quenches from $T_i \rightarrow \infty$ to $T \leq T_s$, where $T_s$ is the (pseudo)-spinodal temperature. The goal is to explain why, in the large-$q$ limit, the low-temperature dynamics freezes on some lattices while, on others, the equilibrium configuration is easily reached. The cubic ($3d$) and the triangular ($2d$) lattices are analysed in detail. We show that the dynamics blocks when lattices have acyclic \textit{unitary structures} while the system goes to the equilibrium when these are cyclic, no matter the coordination number ($z$) of the particular considered lattice.