M. Aizenman et P. Contucci, ON THE STABILITY OF THE QUENCHED STATE IN MEAN-FIELD SPIN-GLASS MODELS, Journal of statistical physics, 92(5-6), 1998, pp. 765-783
While the Gibbs states of spin-glass models have been noted to have an
erratic dependence on temperature, one may expect the mean over the d
isorder to produce a continuously varying ''quenched state.'' The assu
mption of such continuity in temperature implies that in the infinite-
volume limit the state is stable under a class of deformations of the
Gibbs measure. The condition is satisfied by the Parisi Ansatz, along
with an even broader stationarity property. The stability conditions h
ave equivalent expressions as marginal additivity of the quenched free
energy. Implications of the continuity assumption include constraints
on the overlap distribution, which are expressed as the vanishing of
the expectation value for an infinite collection of multi- overlap pol
ynomials. The polynomials can be computed with the aid of a real-repli
ca calculation in which the number of replicas is taken to zero.