A self-consistent Ornstein-Zernike approximation for the Edwards-Anderson spin-glass model

We propose a self consistent Ornstein-Zernike approximation for studying th Edwards Anderson spin glass model. By performing two Legendre transforms i n replica space. We introduce a Gibbs free energy depending on both the mag netizations and the overlap order parameters. The correlation functions and the thermodynamics are then obtained from the solution of a set of coupled partial differential equations. The approximation becomes exact in the lim it of infinite dimension and it provides a potential route for study the st ability of the high-temperature phase against replica-symmetry breaking flu ctuations in finite dimensions. As a first step, we present the predictions for the freezing temperature T-f and for the zero-field thermodynamic prop erties and correlation length above T-f as a function of dimensionality.