# The grand canonical ABC model: a reflection asymmetric mean-field Potts model

@article{Barton2011TheGC, title={The grand canonical ABC model: a reflection asymmetric mean-field Potts model}, author={J. C. Barton and Joel L Lebowitz and E. R. Speer}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2011}, volume={44}, pages={065005} }

We investigate the phase diagram of a three-component system of particles on a one-dimensional filled lattice, or equivalently of a one-dimensional three-state Potts model, with reflection asymmetric mean-field interactions. The three types of particles are designated as A, B and C. The system is described by a grand canonical ensemble with temperature T and chemical potentials TλA, TλB and TλC. We find that for λA = λB = λC the system undergoes a phase transition from a uniform density to a…

## 9 Citations

Phase Diagram of a Generalized ABC Model on the Interval

- Mathematics
- 2011

We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site i=1,…,N is occupied by a particle of type α=A,B,C, with the average density…

Phase diagram of the ABC model with nonconserving processes

- Physics
- 2010

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…

Anomalous long-range correlations at a non-equilibrium phase transition

- Physics
- 2012

Non-equilibrium diffusive systems are known to exhibit long-range correlations, which decay like the inverse 1/L of the system size L in one dimension. Here, taking the example of the ABC model, we…

Ensemble inequivalence: Landau theory and the ABC model

- Physics
- 2012

It is well known that systems with long-range interactions may exhibit different phase diagrams when studied within two different ensembles. In many of the previously studied examples of ensemble…

Phase diagram of the ABC model with nonequal densities

- Physics
- 2011

The ABC model is a driven diffusive exclusion model, composed of three species of particles that hop on a ring with local asymmetric rates. In the weak asymmetry limit, where the asymmetry vanishes…

Phase diagram of the repulsive Blume–Emery–Griffiths model in the presence of an external magnetic field on a complete graph

- Physics
- 2021

Using the repulsive Blume–Emery–Griffiths model, we compute the phase diagram in three field spaces, temperature (T), crystal field (Δ), and magnetic field (H) on a complete graph in the canonical…

Phase diagram and density large deviations of a nonconserving ABC model.

- PhysicsPhysical review letters
- 2012

In the limit of slow nonconserving processes, the large deviation function of the overall particle density can be computed by making use of the steady-state density profile of the conserving model.

Phase Fluctuations in the ABC Model

- Physics
- 2011

We analyze the fluctuations of the steady state profiles in the modulated phase of the ABC model. For a system of L sites, the steady state profiles move on a microscopic time scale of order L3. The…

Fluctuations de courant hors d'équilibre

- Physics
- 2012

Les systemes hors d'equilibre sont souvent caracterises par la presence d'un courant, d'energie ou de particules, qui brise le bilan detaille. Dans ces systemes, les outils traditionnels de la…

## References

SHOWING 1-10 OF 25 REFERENCES

Phase diagram of the ABC model with nonconserving processes

- Physics
- 2010

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…

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

- PhysicsPhysical review letters
- 2010

A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, and the model is found to exhibit two distinct phase diagrams, corresponding to the canonical and grand canonical ensembles, as expected in long-range interacting systems.

Phase Diagram of the ABC Model on an Interval

- Mathematics
- 2009

The three species asymmetric ABC model was initially defined on a ring by Evans, Kafri, Koduvely, and Mukamel, and the weakly asymmetric version was later studied by Clincy, Derrida, and Evans. Here…

Phase transition in the ABC model.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

This work considers the weak asymmetry regime q=exp(-beta/N), where N is the system size, and study how the disordered state is approached, and finds that the system exhibits a second-order phase transition at some nonzero beta(c) in the case of equal densities.

Phase Separation and Coarsening in One-Dimensional Driven Diffusive Systems: Local Dynamics Leading to Long-Range Hamiltonians

- Physics
- 1998

A driven system of three species of particles diffusing on a ring is studied in detail. The dynamics is local and conserves the three densities. A simple argument suggesting that the model should…

Strong phase separation in a model of sedimenting lattices

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics.

Towards a Nonequilibrium Thermodynamics: A Self-Contained Macroscopic Description of Driven Diffusive Systems

- Physics
- 2009

In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple…

Mean-field theory of the many component Potts model

- Physics
- 1974

A mean-field theory of the q-component Potts model is given. The transition is first order for q>or=3. For large q the mean-field results agree with all the known exact results in two dimensions for…

PHASE SEPARATION IN ONE-DIMENSIONAL DRIVEN DIFFUSIVE SYSTEMS

- Physics
- 1998

Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot 76100, Israel(February 7, 2008)A driven diﬀusive model of three types of particles that exhibits phase separation…