Ising spin glasses in the effective-interaction-approximation

Abstract

Using an effective-interaction-approximation we study the critical lines of the Harris and (± 1)-Ising spin glasses. For the square lattice we recover the exact results of Harris Tc(η)/Tc(0) = 1 - 0.311 6 η2 and Domany Tc(p)/ Tc(1) = 1 - 3.209(1 - p). The critical concentration for ferromagnetism pc1 is in good agreement with known results and tends to its mean-field value pc1 = 1/2 when z, the coordination number, tends to infinity. Non-alternate lattices present a retrograde critical line, typical of annealed disorder, in the single-bond approximation. A cluster extension of the method on the triangular and honeycomb lattices indicates that this behaviour is unphysical for quenched disorder