Phase Transition in the ABC Model

TL;DR

This paper investigates the phase transition behavior of the ABC model in the weak asymmetry regime, deriving exact results for equal densities and mean field predictions for unequal densities, revealing a second order phase transition.

Contribution

It provides an exact large deviation functional for the phase transition in the ABC model and analyzes mean field equations for unequal densities, extending understanding of phase behavior.

Findings

Second order phase transition at _c = 2 7 4 6.

Exact large deviation functional derived for equal densities.

Mean field analysis predicts phase behavior for unequal densities.

Abstract

Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring, shows anomalous coarsening into a phase separated steady state. In the limiting case in which the dynamics is symmetric and the parameter $q$ describing the asymmetry tends to one, no phase separation occurs and the steady state of the system is disordered. In the present work we consider the weak asymmetry regime $q=\exp{(-\beta/N)}$ where $N$ is the system size and study how the disordered state is approached. In the case of equal densities, we find that the system exhibits a second order phase transition at some nonzero $\beta_c$. The value of $\beta_c = 2 \pi \sqrt{3}$ and the optimal profiles can be obtained by writing the exact large deviation functional. For nonequal densities, we write down mean field equations and analyze some of their predictions.