Local scale-invariance and ageing in noisy systems

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.

Latex2e, 45 pages, no figures, final form

References in corpus (3)

• Scaling of the linear response in simple ageing systems without disorder
• Bona Fide Thermodynamic Temperature in Nonequilibrium Kinetic Ising Models
• General Solutions for Multispin Two-Time Correlation and Response Functions in the Glauber-Ising Chain

Cited by in corpus (6)

• Two-time autocorrelation function in phase-ordering kinetics from local scale-invariance
• Ageing phenomena without detailed balance: the contact process
• Ageing in the critical contact process: a Monte Carlo study
• Ageing and dynamical scaling in the critical Ising spin glass
• On the scaling and ageing behaviour of the alternating susceptibility in spin glasses and local scale-invariance
• On the dynamical symmetric algebra of ageing: Lie structure, representations and Appell systems