Autocorrelation functions in phase-ordering kinetics from local scale-invariance

TL;DR

This paper reviews how local scale-invariance extends dynamical scaling to calculate autocorrelation functions in phase-ordering kinetics, supported by exact solutions and simulations across various models.

Contribution

It introduces a novel extension of conformal algebra to d+2 dimensions for analyzing autocorrelations in non-equilibrium systems with z=2.

Findings

Explicit autocorrelation forms derived for several models

Validation through simulations of 2D Ising and Potts models

Discussion of generalizations to other dynamical exponents z

Abstract

The explicit calculation of the scaling form of the two-time autocorrelation function in phase-ordering kinetics and in those cases of non-equilibrium critical dynamics where the dynamical exponent z=2 through the extension of dynamical scaling to local scale-invariance is reviewed. Conceptually, this mainly requires an extension from the usually considered d-dimensional ageing or Schr\"odinger algebras to a new kind of representation of the conformal algebra in d+2 dimensions. Explicit tests in several exactly solved models of simple magnets and through simulations in the 2D Ising and q-states Potts models (q=2,3,8) quenched to T<T_c are presented and the extension to systems with non-equilibrium steady-states is discussed through two exactly solvable models as well. In the context of surface growth models, possible generalizations for a dynamical exponent z=4 and beyond are discussed.