Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution

Details Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution

2000-10-20

arxiv.org/abs/cond-mat/0010319v1

Physica A 294 (2001) 362-374

Physics

Condensed Matter

Statistical Mechanics

10 pages, no figures

Scientific paper

10.1016/S0378-4371(01)00032-2

We solve the Langevin dynamics of d-dimensional ferromagnetic spherical models with interactions that decay with distance as r^-(d+sigma). The long time dynamics of correlations and responses are studied in the different dynamical regimes and the validity of fluctuation-dissipation relations (or its violation) are shown. In particular, we show that the fluctuation-dissipation ratio X(t+t_w,t_w) is assymptotically a function only of the waiting time t_w in the aging regime and that X -> 0 as t_w -> oo . The results are valid in any finite dimension d and for 0 < sigma < 2, where short range behaviour is recovered. We also solve the T=0 Cahn-Hilliard dynamics of this model (conserved order parameter). An analysis of the multiscaling behaviour of the autocorrelation function is presented.

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