Spin Glass Identities and the Nishimori Line

TL;DR

This paper proves a family of identities involving overlaps and magnetizations in spin glass models, valid on the Nishimori line and in the thermodynamic limit, enhancing understanding of their statistical properties.

Contribution

It establishes new identities for asymmetric spin glass models on the Nishimori line, extending known results to more general settings.

Findings

Identities hold pointwise on the Nishimori line

Identities hold in integral average in the general case

Results improve understanding of spin glass expectations

Abstract

For a general spin glass model with asymmetric couplings we prove a family of identities involving expectations of generalized overlaps and magnetizations in the quenched state. Those identities holds pointwise in the Nishimori line and are reached at the rate of the inverse volume while, in the general case, they can be proved in integral average.