Long-range correlations and ensemble inequivalence in a generalized ABC model

Abstract

A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For equal average densities of the three species, both dynamical models are demonstrated to exhibit detailed balance with respect to a Hamiltonian with long-range interactions. The model is found to exhibit two distinct phase diagrams, corresponding to the canonical (density-conserving) and grand canonical (density nonconserving) ensembles, as expected in long-range interacting systems. The implication of this result to nonequilibrium steady states, such as those of the ABC model with unequal average densities, are briefly discussed.

4 pages, 2 figures. v2: minor changes with an added reference, published version

References in corpus (2)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Discontinuous condensation transition and nonequivalence of ensembles in a zero-range process

Cited by in corpus (20)

• Phase fluctuations in the ABC model
• Aging processes in systems with anomalous slow dynamics
• Phase diagram and density large deviations of a nonconserving ABC model
• Current fluctuations at a phase transition
• Ensemble Inequivalence in the Ferromagnetic p-spin Model in Random Fields
• Phase diagram of the ABC model with nonconserving processes
• Ensemble Inequivalence and the Spin-Glass Transition
• Ensemble inequivalence : Landau theory and the ABC model
• Phase transitions in Thirring's model
• The grand canonical ABC model: a reflection asymmetric mean field Potts model
• Phase diagram of the ABC model with nonequal densities
• Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions
• Weak Chaos from Tsallis Entropy
• Many-body spin glasses in the microcanonical ensemble
• Anomalous long-range correlations at a non-equilibrium phase transition
• Phase diagram of the repulsive Blume-Emery-Griffiths model in the presence of external magnetic field on a complete graph
• Energy Storage in Steady States under Cyclic Local Energy Input
• Relaxation processes in a system with logarithmic growth
• Ensemble equivalence in spin systems with short-range interactions
• Ensemble Equivalence for Counterion Condensation on a Two Dimensional Charged Disc