AB model with coalescence: Mean field and Monte Carlo simulations

We study a competitive two-species (A and B) reaction-diffusion model on a bipartite square lattice, where cooperative interactions lead to either particle coalescence or dispersal. The model is controlled by a coalescence-dispersion parameter g and a maximum site occupancy per species, n_{o}. We investigate the system's phase transitions from an active to an absorbing state using both a site-based mean field approximation and Monte Carlo (MC) simulations. For single occupancy (n_{o}=1), we find a discontinuous, first-order phase transition at a transition point g_{c}=1. The mean field calculations reveal a manifold of solutions at this point, leading to bistability between an active phase and an ordered, chessboardlike absorbing state-a mechanism of dynamic bistability confirmed by simulations. For multi-occupancy cases (n_{o}≥2), the transition remains first order but occurs for g_{c}<1. Here, the absorbing phase is an infinitely degenerate manifold of disordered, jammed configurations. MC simulations show that the transition point g_{c} increases with n_{o} for n_{o}≥2. This trend seems to be driven by the role of coalescence as an antisegregation mechanism. As n_{o} increases, the system becomes denser, enhancing this mixing effect and thus requiring a stronger dispersal probability (a higher g_{c}) to induce the transition to the segregated absorbing state. In this model, the site's storage capacity strongly alters the macroscopic transition mechanism.