Local scale invariance and its applications to strongly anisotropic critical phenomena

TL;DR

This paper reviews the extension of dynamical scaling to local scale invariance, predicting two-point functions and confirming these predictions in Lifshitz points and non-equilibrium ageing phenomena.

Contribution

It introduces a generalized framework of local scale invariance applicable to strongly anisotropic critical phenomena, including special cases like Schrödinger invariance.

Findings

Predicted two-point functions match observed data in Lifshitz points.

Confirmed local scale invariance predictions in ageing phenomena of kinetic Ising models.

Established two types of local scale invariance for different dynamical exponents.

Abstract

The generalization of dynamical scaling to local scale invariance is reviewed. Starting from a recapitulation of the phenomenology of ageing phenomena, the generalization of dynamical scaling to local scale transformation for any given dynamical exponent $z$ is described and the two distinct types of local scale invariance are presented. The special case $z=2$ and the associated Ward identity of Schr\"odinger invariance is treated. Local scale invariance predicts the form of the two-point functions. Existing confirmations of these predictions for (I) the Lifshitz points in spin systems with competing interactions such as the ANNNI model and (II) non-equilibrium ageing phenomena as occur in the kinetic Ising model with Glauber dynamics are described.