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

Ana L. N. Dias; Ronald Dickman; Tiago Venzel Rosembach

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arXiv · 2604.22536

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

Ana L. N. Dias·Ronald Dickman·Tiago Venzel Rosembach

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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.

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Ana L. N. Dias, Ronald Dickman, Tiago Venzel Rosembach. 2026-04-24. Mean-Field Theory for the Three-State Active Lattice Gas Model. https://arxiv.org/abs/2604.22536

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