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. Nonperturbative phenomena are present when 1 ≪ Δ H ≪ N , being Δ H the coupling Hamiltonian and N the system size. In this intermediate-coupling region, the effect is related to finite-size free-energy corrections in mean-field spin-glass models and to 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.
Franz et al. (Thu,) studied this question.