Three-state active lattice gas: a discrete Vicseklike model with excluded volume

TL;DR

This study introduces a three-state active lattice gas model with excluded volume on a triangular lattice, revealing complex phase transitions and spatial patterns, including continuous and discontinuous transitions depending on density.

Contribution

It presents a novel discrete active matter model with three orientations, analyzing phase behavior and transitions, including symmetry with the Potts model and detailed transition characterizations.

Findings

Ordered condensed structures coexist with vapor at certain densities.

The model exhibits a continuous phase transition at full occupancy with Potts model universality.

At low density, the transition is discontinuous with hysteresis and nonmonotonic Binder cumulant behavior.

Abstract

We study a discrete-space model of active matter with excluded volume. Particles are restricted to the sites of a triangular lattice, and can assume one of three orientations. Varying the density and noise intensity, Monte Carlo simulations reveal a variety of spatial patterns. Ordered states occur in the form of condensed structures, which (away from the full occupancy limit) coexist with a low-density vapor. The condensed structures feature low particle mobility, particularly those that wrap the system via the periodic boundaries. As the noise intensity is increased, dense structures give way to a disordered phase. We characterize the parameter values associated with the condensed phases and perform a detailed study of the order-disorder transition at (1) full occupation and (2) at a density of 0.1. In the former case, the model possesses the same symmetry as the three-state Potts model and exhibits a continuous phase transition, as expected, with critical exponents consistent with those of the associated Potts model. In the low-density case, the transition is clearly discontinuous, with strong dependence of the final state upon the initial configuration, hysteresis,and nonmonotonic dependence of the Binder cumulant upon noise intensity.