GAUGE-INVARIANT METHOD FOR THE +/- J SPIN-GLASS MODEL

This paper deals with the +/- J Ising model in two dimensions in the general case where there is a concentration p of negative bonds. We are particularly interested in exploring the Pfaffian (or combinatorial) method for treating this problem because a Green's-function formalism can be developed in which the frustration manifests itself in a gauge-invariant form through temperature-dependent singularities. We describe the formalism in detail and show how the disappearance of ferromagnetic order at a critical value of p can be related to a transition from localized to extended states analogous to the Anderson transition. Calculations are performed for the ground-state energy and entropy, which are obtained exactly for large samples. We introduce an exponent rho that describes the underlying singularity structure of the Green's-function formalism and we show how this is related to the exponent of the spin-spin correlation function of the Ising problem. A value for this exponent of eta = 0.4 is obtained.