Replica Symmetric Solutions in the Ising Spin Glass: The Tree Approximation

Abstract

We consider an Ising spin glass on a d-dimensional hypercubic lattice with a general bond distribution in the tree approximation. Using closed-form expressions for the "masses" we give the boundaries of the symmetric stable region for the dilute spin glass. We also show that the system can be described using an order parameter function as Mézard and Parisi have done for optimization problems.