On logarithmic extensions of local scale-invariance

TL;DR

This paper introduces a logarithmic extension of local scale-invariance applicable to non-equilibrium ageing phenomena, deriving covariant two-point functions and comparing them with simulation data.

Contribution

It proposes a novel logarithmic extension of local scale-invariance that incorporates Jordan cells for scaling dimensions, expanding the theoretical framework for ageing phenomena.

Findings

Derived covariant two-point functions for the logarithmic extension.

Compared theoretical predictions with simulation data for ageing systems.

Validated the extended framework against non-equilibrium ageing data.

Abstract

Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schr\"odinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena.