Toward a Classification of Stochastically Stable Quenched Measures,
2003, v.9, Issue 2, 167-176
In this short note we study the fourth order consequences of the stochastic stability property for mean field spin glass models introduced in [M. Aizenman, P. Contucci, On the stability of the quenched state in mean field spin glass models, J. Stat. Phys., 1998, 92, (5/6), 765-783. Available at cond-mat/9712129]. We show that due to a remarkable cancellation mechanism it reduces to the well known second order version as predicted by the Parisi replica-equivalent ansatz.
Keywords: mean field spin glass,stochastic stability