Phase diagram of the ABC model with nonequal densities

TL;DR

This paper derives the exact phase diagram for the ABC model with unequal densities, revealing the nature of phase transitions in a driven diffusive system with three particle species.

Contribution

It provides the exact hydrodynamic solutions and phase diagram for the ABC model with arbitrary densities, extending understanding beyond equal density cases.

Findings

Exact density profiles for arbitrary densities

Complete phase diagram including first order transitions

Insights into phase behavior with nonequal densities

Abstract

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 with the length of the system, the model exhibits a phase transition between a homogenous state and a phase separated state. We derive the exact solution for the density profiles of the three species in the hydrodynamic limit for arbitrary average densities. The solution yields the complete phase diagram of the model and allows the study of the nature of the first order phase transition found for average densities that deviate significantly from the equal densities point.