Ageing, dynamical scaling and conformal invariance

TL;DR

This paper develops a theoretical framework linking conformal invariance and dynamical scaling, identifying local scale invariances that determine two-point functions, and confirms these predictions through tests on the 3D ANNNI model and ferromagnetic ageing phenomena.

Contribution

It introduces two types of local scale invariance acting as dynamical symmetries in non-local free field theories, extending the understanding of scaling behaviors in complex systems.

Findings

Two types of local scale invariance are identified.

Two-point functions are fully determined by local scale invariance.

Predictions are validated in the 3D ANNNI model and ferromagnetic ageing experiments.

Abstract

Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local free field theories. The scaling form of two-point functions is completely fixed by the requirement of local scale invariance. These predictions are confirmed through tests in the 3D ANNNI model at its Lifshitz point and in ageing phenomena of simple ferromagnets, here studied through the kinetic Ising model with Glauber dynamics.