Simplicity of the spherical spin-glass model

Abstract

We revisit an approach to the replica-based analysis of the spherical spin-glass model that makes use of a mapping of the problem onto a one-dimensional interacting charge system. A saddle point approximation leads to the conclusion that the interaction between charges is irrelevant in the thermodynamic limit, and as a consequence, that there is no nontrivial correlation between replicas for this model. This allows us to show that quenched and annealed disorder averages agree for the spherical spin glass. We demonstrate this result within two different mathematical frameworks, and we also relate our analysis to the conclusions that follow from the replica symmetry ansatz.