# 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}
}
• Published 6 October 2010
• Physics
• Journal of Physics A: Mathematical and Theoretical
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

### 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.

• Physics
Physical 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

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

### 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

## References

SHOWING 1-10 OF 25 REFERENCES

### 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.

• Physics
Physical 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

• Physics
Physical 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

### Notes on the Statistical Mechanics of Systems with Long-Range Interactions

Thermodynamic and dynamical properties of systems with long range pairwise interactions (LRI) which decay as 1/r^{d+\sigma} at large distances r in $d$ dimensions are reviewed in these Notes. Two

### Three-state Potts model and anomalous tricritical points

• Physics
• 1973
Thirteen terms are presented of the low-temperature series for the free energy of the three-state Potts model in arbitrary external fields. Extrapolation of the series for specific heat, order