Disordered Systems Glasses

Theoretical Aspects of Realistic Spin Glass Models

R. Hilfer

in: New Trends in Magnetism
edited by: M.D. Coutinho-Filho and S.M. Rezende
World Scientific Publ.Co., Singapore, 32 (1989)

submitted on
Thursday, July 27, 1989

This note investigates the universality of spin glass models by calculating the distribution of instantaneous local magnetic fields, p(h). It is found that short range Ising models with Gaussian bond disorder fall into a different universality class than realistic models with RKKY-interactions and randomly positioned spins. The result is obtained from an analysis of p(h) at high temperatures where thelocal fields are sums of independent random variables. It is found that for realistic models these sums are in general not governed by the central limit theorem. In three dimensions a cutoff Cauchy distribution is obtained for p(h) instead of a Gaussian distribution. In general p(h) is a cutoff stable law whose characteristic exponent depends strongly on the dimension and the decay of the interactions. As a consequence a new short range model is proposed for dilute metallic spin glasses in three dimensions in which the bond disorder is taken to be a cutoff Cauchy distribution instead of a Gaussian. Preliminary considerations indicate a much smoother specific heat for models in this universality class and suggest the existence of strong precursor effects in qualitative agreement with experiment.

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