Spin Glass Identities and the Nishimori Line

Pierluigi Contucci, Cristian Giardina, Hidetoshi Nishimori

Published 2008-05-06, updated 2008-05-13Version 2

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.