Local scale-invariance and ageing in noisy systems

Alan Picone (1) , Malte Henkel (1)

1 LPM - Laboratoire de physique des matériaux

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.

Domaines: Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]

Alan Picone, Malte Henkel. Local scale-invariance and ageing in noisy systems. Nuclear Physics B, 2004, 688, pp.217-265. ⟨10.1016/j.nuclphysb.2004.03.028⟩. ⟨hal-00132139⟩