Dynamic modes of active Potts models with factorizable numbers of states

TL;DR

This paper investigates the complex nonequilibrium dynamics of multi-state Potts models, revealing new dynamic modes such as skipping states and spiral waves, influenced by factorizable state numbers and contact energies.

Contribution

It introduces novel dynamic modes in Potts models with factorizable state numbers, including skipping states and spiral wave patterns, expanding understanding of nonequilibrium phase behavior.

Findings

Cyclic phase changes observed at low and high energies for all q.

Emergence of skipping states depending on contact energies.

Identification of spiral wave modes in q=6 Potts models.

Abstract

We studied the long-term nonequilibrium dynamics of $q$-state Potts models with $q=4$, $5$, $6$, and $8$ using Monte Carlo simulations on a two-dimensional square lattice. When the contact energies between the nearest neighbors for the standard Potts models are used, cyclic changes in the $q$ homogeneous phases and $q$-state coexisting wave mode appear at low and high flipping energies, respectively, for all values of $q$. However, for a factorizable $q$ value, dynamic modes with skipping states emerge, depending on the contact energies. For $q=6$, a spiral wave mode with three domain types (one state dominant or two states mixed) and cyclic changes in three homogeneous phases are found. Although three states can coexist spatially under thermal equilibrium, the scaling exponents of the transitions to the wave modes are modified from the equilibrium values.