Phase Separation in One-Dimensional Driven Diffusive Systems

TL;DR

This paper introduces a driven diffusive model with three particle types on a ring, demonstrating phase separation through analytical calculations of the steady state and correlation functions, especially when densities are equal.

Contribution

It presents a new three-species driven diffusive model with local dynamics and long-range interactions, analyzing phase separation and steady state properties.

Findings

Model exhibits phase separation at equal densities.

Steady state obeys detailed balance with a long-range Hamiltonian.

Analytical bounds on correlation functions support phase separation.

Abstract

A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the three densities are equal, it is shown that the model obeys detailed balance. The Hamiltonian governing the steady state distribution in this case is given and is found to have long range asymmetric interactions. The partition sum and bounds on some correlation functions are calculated analytically demonstrating phase separation.