Dynamics due to competitive flip cycles in active Potts models

TL;DR

This paper explores how competing cyclic loops at each site in active Potts models influence pattern formation, revealing energy-dependent transitions between spiral waves, homogeneous cycling, and dominant states.

Contribution

It introduces the study of multi-cycle competition in active Potts models, showing how flip energies control complex spatiotemporal patterns and state dominance.

Findings

Multiple three-state cycles produce simultaneous spiral waves at high energies.

Lower energies lead to stochastic switching between a few types or homogeneous cycling.

Six-state networks show a dominant state with occasional domain formation at intermediate energies.

Abstract

Nonequilibrium spatiotemporal patterns have been extensively studied. However, a single oscillator or cyclic loop of states is typically employed at each site in theories and simulations. Here, we investigate how competition among multiple identical cyclic loops at each site alters patterns. We simulate active Potts models with standard Potts interactions between neighboring sites in two-dimensional square lattices. When multiple three-state cycles exist in state flips, such as in octahedral and square-antiprism networks, all types of spiral waves comprising the three states are formed simultaneously at high flip energies. However, at lower energies, only one or a few types emerge and switch stochastically into different types. At even lower energies, cyclic changes in single-state dominant homogeneous phases emerge [homogeneous cycling (HC) mode]. At intermediate flip energies, the spiral wave and HC modes temporally coexist in small systems but do not switch between each other in large systems. Conversely, when multiple four-state cycles exist in six-state and cubic networks, one state remains dominant for the entire range of flip energies, whereas the other states occasionally form domains at intermediate flip energies. Therefore, the number of spatially coexisting states can be controlled using flip networks and energies.