Local scale-invariance and ageing in noisy systems

TL;DR

This paper investigates how noise affects long-time ageing dynamics in ferromagnetic systems, showing that certain response functions remain noise-independent and deriving explicit scaling forms validated across multiple models.

Contribution

It demonstrates that local scale-invariance governs the ageing behavior in noisy systems with z=2, providing exact forms for response and correlation functions.

Findings

Response functions are noise-independent under certain invariance conditions.

Explicit scaling forms for autocorrelation functions are derived.

Results are validated across multiple models including the spherical and XY models.

Abstract

The influence of the noise on the long-time ageing dynamics of a quenched ferromagnetic spin system with a non-conserved order parameter and described through a Langevin equation with a thermal noise term and a disordered initial state is studied. If the noiseless part of the system is Galilei-invariant and scale-invariant with dynamical exponent z=2, the two-time linear response function is independent of the noise and therefore has exactly the form predicted from the local scale-invariance of the noiseless part. The two-time correlation function is exactly given in terms of certain noiseless three- and four-point response functions. An explicit scaling form of the two-time autocorrelation function follows. For disordered initial states, local scale-invariance is sufficient for the equality of the autocorrelation and autoresponse exponents in phase-ordering kinetics. The results for the scaling functions are confirmed through tests in the kinetic spherical model, the spin-wave approximation of the XY model, the critical voter model and the free random walk.