Exact Solution of a Phase Separation Model with Conserved Order Parameter Dynamics

TL;DR

This paper presents an exact solution to a phase separation model with conserved order parameter, using a novel rate-equation approach to analyze zero-temperature particle exchange dynamics on a lattice.

Contribution

It introduces a new exact analytical method for solving a lattice-based phase separation model with conserved order parameters.

Findings

The model reaches a frozen state at large times.

The structure of the frozen state depends on initial conditions.

The solution applies to a zero-temperature Kawasaki-type process.

Abstract

Pairwise particle-exchange model on a linear lattice is solved exactly by a new rate-equation method. Lattice sites are occupied by particles A and B which can exchange irreversibly provided the local energy in reduced. Thus, the model corresponds to a zero-temperature Kawasaki-type phase separation process. Due to local order-parameter conservation, the dynamics reaches a frozen state at large times, the structure of which depends on the initial conditions.