Kawasaki-type Dynamics: Diffusion in the kinetic Gaussian model

TL;DR

This paper generalizes Kawasaki's spin-pair exchange dynamics to a redistribution mechanism, deriving an exact diffusion equation for the kinetic Gaussian model and revealing universal critical dynamic behavior independent of dimensionality.

Contribution

It introduces a unified redistribution mechanism for order-parameter-conserved processes and applies it to derive exact diffusion dynamics in the Gaussian model.

Findings

Critical slowing down observed near the critical point

Critical dynamic exponent z=2 independent of dimensionality

Universal behavior regardless of the specific mechanism

Abstract

In this article, we retain the basic idea and at the same time generalize Kawasaki's dynamics, spin-pair exchange mechanism, to spin-pair redistribution mechanism, and present a normalized redistribution probability. This serves to unite various order-parameter-conserved processes in microscopic, place them under the control of a universal mechanism and provide the basis for further treatment. As an example of the applications, we treated the kinetic Gaussian model and obtained exact diffusion equation. We observed critical slowing down near the critical point and found that, the critical dynamic exponent z=1/nu=2 is independent of space dimensionality and the assumed mechanism, whether Glauber-type or Kawasaki-type.