Phase diagram of the ABC model with nonconserving processes

TL;DR

This paper analyzes the phase diagram of an extended ABC model with vacancies and nonconserving processes, revealing phase separation and ensemble inequivalence due to long-range interactions, supported by analytical and simulation results.

Contribution

It introduces a generalized ABC model with nonconserving processes and long-range interactions, providing exact phase diagrams and stability analysis.

Findings

Both models show a transition from homogeneous to phase-separated states.

Phase diagrams differ between conserving and nonconserving models, indicating ensemble inequivalence.

Monte-Carlo simulations support the analytical results.

Abstract

The three species ABC model of driven particles on a ring is generalized to include vacancies and particle-nonconserving processes. The model exhibits phase separation at high densities. For equal average densities of the three species, it is shown that although the dynamics is {\it local}, it obeys detailed balance with respect to a Hamiltonian with {\it long-range interactions}, yielding a nonadditive free energy. The phase diagrams of the conserving and nonconserving models, corresponding to the canonical and grand-canonical ensembles, respectively, are calculated in the thermodynamic limit. Both models exhibit a transition from a homogeneous to a phase-separated state, although the phase diagrams are shown to differ from each other. This conforms with the expected inequivalence of ensembles in equilibrium systems with long-range interactions. These results are based on a stability analysis of the homogeneous phase and exact solution of the hydrodynamic equations of the models. They are supported by Monte-Carlo simulations. This study may serve as a useful starting point for analyzing the phase diagram for unequal densities, where detailed balance is not satisfied and thus a Hamiltonian cannot be defined.