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.