Mean-Field Theory for the Three-State Active Lattice Gas Model

TL;DR

This paper develops a mean-field model with spatial structure for a simplified three-state active matter system, analyzing stability and phase transitions through numerical integration and simulations.

Contribution

It introduces a mean-field approach with spatial structure for a simplified active matter model, revealing complex stability and transition phenomena.

Findings

Identification of high-density ordered structures in the density-noise plane

Observation of unexpected transitions between ordered states

Comparison with Monte Carlo simulations confirms some theoretical predictions

Abstract

We develop a mean-field description including spatial structure for a simplified version of the three-state active matter model studied by Venzel et al. (Phys. Rev. E 110, 014109 (2024)). The resulting triangular lattice of coupled nonlinear differential equations are integrated numerically using a fourth-order Runge-Kutta scheme. Starting from various ordered initial configurations, we probe the stability of the corresponding stationary states, revealing the presence of various high-density ordered structures in the density(\r{ho})-noise({\eta}) plane. The results are compared with Monte Carlo simulations of the simplified model, yielding, in certain cases, unexpected transitions between ordered configuration types.