Phase diagram of the ABC model with nonconserving processes

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.

32 page, 7 figures. The paper was presented at Statphys24, held in Cairns, Australia, July 2010

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• Phase diagram of the repulsive Blume-Emery-Griffiths model in the presence of external magnetic field on a complete graph
• Anomalous long-range correlations at a non-equilibrium phase transition
• Relaxation processes in a system with logarithmic growth
• Phase diagram of a generalized ABC model on the interval