Local independence in mean-field spin glasses

Timothy L. H. Wee, Sekhar Tatikonda

Published 2022-12-30Version 1

We present a new approach to local independence in spin glasses, i.e. the phenomenon that any fixed subset of coordinates is asymptotically independent in the thermodynamic limit. The approach generalizes the rigorous cavity method from Talagrand by considering multiple cavity sites. Under conditions of thin-shell and overlap concentration, a general random projections result, of standalone interest, characterizes the joint distributions of the cavity fields and reveals their asymptotic independence. The framework is general enough to encompass the classical and soft spin ($[-1,1]$) Sherrington-Kirkpatrick models, as well as the Gardner spin glasses.