A Mean-Field Approach for Inhomogeneous Spin-Glass Models
A mean-field replica-type theory is presented for long-range Ising spin-glasses whose interactions can be written in the form J ij = J ij I J ij SK , where J SK is a quenched Gaussian interaction, as in the SK spin-glass, and J I is a deterministic matrix which defines the structure or inhomogeneity of the model and must have a finite rank in the thermodynamic limit. The spin-glass model proposed by Franz, Parisi and Virasoro ( Europhys. Lett. , 17 (1992) 5) can be written in this form, with J I having rank 2, and is used as a case study to illustrate our theory. In the context of replica theory we also consider the stable states of this model, which appear continuously as the temperature is lowered.
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