Overlap locking and non-perturbative effects in spin glasses

TL;DR

This paper investigates how coupling affects order parameter locking in spin glasses, analyzing non-perturbative effects and finite-size corrections through mean-field and hierarchical models.

Contribution

It provides a combined analytical and numerical study of coupling-induced locking and non-perturbative phenomena in spin glasses, including critical exponents.

Findings

Finite-size free-energy corrections relate to the locking effect.

Critical exponents for finite-volume corrections are computed.

Decay of correlations in the Dyson hierarchical model is characterized.

Abstract

We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this effect depends on the strength of the coupling between the two systems. Non-perturbative phenomena are present when $1 \ll \Delta H \ll N$, being $\Delta H$ the coupling Hamiltonian and $N$ the size of the system. In this intermediate-coupling region, the effect is related to finite-size free-energy corrections and to the correlations in the Dyson hierarchical spin glass, a model that mimics the physics of finite-dimensional systems. We study this phenomenon in the mean-field approach, both analytically and numerically, and we finally compute the critical exponents for finite-volume corrections in mean-field theory and for the decay of correlations in the Dyson hierarchical model.