The role of the interaction matrix in mean-field spin glasses

TL;DR

This paper investigates how the eigenvalue spectrum of interaction matrices influences the phase transition in mean-field 2-spin Ising spin glasses, using analytical, numerical, and simulation methods.

Contribution

It introduces a replica approach for averaging over O(N) invariant disorder and links the transition nature to eigenvalue spectra.

Findings

Eigenvalue spectrum determines the spin glass transition type.

Analytic replica approach effectively averages over O(N) disorder.

Simulation results confirm theoretical predictions across system sizes.

Abstract

Mean-field models of 2-spin Ising spin glasses with interaction matrices taken from ensembles which are invariant under O(N) transformations are studied. A general study shows that the nature of the spin glass transition can be deduced from the eigenvalue spectrum of the interaction matrix. A simple replica approach is derived to carry out the average over the O(N) disorder. The analytic results are confirmed by extensive Monte Carlo simulations for large system sizes and by exact enumeration for small system sizes.