Local scale-invariance and ageing in noisy systems

Details Local scale-invariance and ageing in noisy systems Local scale-invariance and ageing in noisy systems

2004-02-06

arxiv.org/abs/cond-mat/0402196v3

Nucl.Phys. B688 (2004) 217-265

Physics

Condensed Matter

Statistical Mechanics

Latex2e, 45 pages, no figures, final form

Scientific paper

10.1016/j.nuclphysb.2004.03.028

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.

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