Numerical Evidence for Continuity of Mean Field and Finite Dimensional Spin Glasses

TL;DR

This paper provides numerical evidence suggesting that disorder-averaged quantities in spin glasses are continuous functions, supporting the applicability of Replica Symmetry Breaking to finite-dimensional models.

Contribution

It introduces a numerical study of an interpolating disordered model, showing smooth disorder averages and supporting RSB in finite dimensions.

Findings

Disorder averages of overlap powers are smooth and show no discontinuity.

Evidence from multiple lattice sizes supports smooth thermodynamic limit behavior.

Quantities on individual disorder realizations exhibit chaotic behavior.

Abstract

We study numerically a disordered model that interpolates among the Sherrington-Kirkpatrick mean field model and the three dimensional Edwards-Anderson spin glass. We find that averages over the disorder of powers of the overlap and of the full $P(q)$ are smooth, and do not show any discontinuity. Different lattice sizes are used to provide evidence for a smooth behavior of disorder averages in the thermodynamic limit. Quantities defined on a given realization of the disorder show a chaotic behavior. Our results support the validity of a Replica Symmetry Breaking description of finite dimensional models.