Glauber Critical Dynamics: Exact Solution of the Kinetic Gaussian Model

TL;DR

This paper provides an exact solution for Glauber critical dynamics of the Gaussian model in three dimensions, revealing a universal dynamical critical exponent consistent across different spatial dimensions.

Contribution

It generalizes the spin transition mechanism in Glauber dynamics and demonstrates the universality of the dynamical critical exponent across dimensions.

Findings

Exact solution for 3D Glauber dynamics of Gaussian model

Universal dynamical critical exponent independent of dimension

Generalized spin transition mechanism in Glauber dynamics

Abstract

In this paper, we have exactly solved Glauber critical dynamics of the Gaussian model on three dimensions. Of course, it is much easy to apply to low dimensional case. The key steps are that we generalize the spin change mechanism from Glauber's single-spin flipping to single-spin transition and give a normalized version of the transition probability . We have also investigated the dynamical critical exponent and found surprisingly that the dynamical critical exponent is highly universal which refer to that for one- two- and three-dimensions they have same value independent of spatial dimensionality in contrast to static (equilibrium) critical exponents.