Spatiotemporal patterns in the active cyclic Potts model

TL;DR

This study explores the complex spatiotemporal behaviors of a nonequilibrium three-state Potts model, revealing various pattern formations and phase coexistences driven by energy parameters through simulations and continuum theory.

Contribution

It introduces a detailed analysis of cyclic and asymmetric conditions in the active Potts model, highlighting novel pattern formations and phase coexistence mechanisms.

Findings

Formation of cycling homogeneous phases and spiral waves at different flipping energies.

Observation of amoeba-like locomotion and phase coexistence under asymmetric conditions.

Energy-dependent emergence of a third phase due to nucleation suppression.

Abstract

The nonequilibrium dynamics of a cycling three-state Potts model is studied on a square lattice using Monte Carlo simulations and continuum theory. This model is relevant to chemical reactions on a catalytic surface and to molecular transport across a membrane. Several characteristic modes are formed depending on the flipping energies between successive states and the contact energies between neighboring sites. Under cyclic symmetry conditions, cycling homogeneous phases and spiral waves form at low and high flipping energies, respectively. In the intermediate flipping energy regime, these two modes coexist temporally in small systems and/or at low contact energies. Under asymmetric conditions, we observed small biphasic domains exhibiting amoeba-like locomotion and temporal coexistence of spiral waves and a dominant non-cyclic one-state phase. An increase in the flipping energy between two successive states, say state 0 and state 1, while keeping the other flipping energies constant, induces the formation of the third phase (state 2), owing to the suppression of the nucleation of state 0 domains. Under asymmetric conditions regarding the contact energies, two different modes can appear depending on the initial state, due to a hysteresis phenomenon.