AB model with coalescence: Mean field and Monte Carlo simulations

Area of Science:

• Statistical Physics
• Complex Systems
• Computational Modeling

Background:

• Reaction-diffusion models are crucial for understanding pattern formation and phase transitions in various systems.
• Bipartite lattices offer unique structures for studying species interactions and spatial dynamics.
• Phase transitions, particularly from active to absorbing states, are fundamental phenomena in statistical mechanics.

Purpose of the Study:

• To investigate the impact of maximum site occupancy (n₀) on phase transitions in a two-species reaction-diffusion model.
• To analyze the interplay between coalescence-dispersion parameter (g) and site capacity in determining system behavior.
• To elucidate the mechanisms driving dynamic bistability and the nature of absorbing states.

Main Methods:

• Site-based mean field approximation for theoretical analysis.
• Monte Carlo (MC) simulations for empirical validation and exploration of complex dynamics.
• Analysis of phase transitions, including order of transition and absorbing state characteristics.

Main Results:

• A first-order phase transition occurs at g_c=1 for single occupancy (n₀=1), exhibiting dynamic bistability between active and ordered absorbing states.
• For multi-occupancy (n₀≥2), the transition remains first-order but shifts to g_c<1, with disordered, jammed absorbing states.
• MC simulations confirm that the transition point (g_c) increases with n₀ for n₀≥2, driven by enhanced mixing effects.

Conclusions:

• Site storage capacity significantly alters the macroscopic transition mechanism in reaction-diffusion systems.
• Coalescence acts as an antisegregation mechanism, with increasing site occupancy promoting mixing and requiring higher dispersal rates for segregation.
• The model demonstrates a rich phase diagram where local rules (site occupancy) lead to distinct macroscopic behaviors.