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

Sergio A. Cannas·Daniel A. Stariolo·Francisco A. Tamarit
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Abstract

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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Sergio A. Cannas, Daniel A. Stariolo, Francisco A. Tamarit. 2000-10-20. Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution. https://doi.org/10.1016/s0378-4371(01)00032-2

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