ON THE COMPUTATION OF STATIC EXPECTATION VALUES FROM DYNAMICS IN SPIN-GLASSES

We discuss the derivation of canonical correlation functions from the dynamic approach in long-range spin-glasses. We argue that such derivations are possible using the saddle-point approximation even in the presence of ergodicity breaking, within the following scenario: a) the dynamical saddle-point solution is not unique at infinite times-scales; b) a single dynamic solution does not yield the measurable correlation functions (e.g. as observed at very long times in a computer simulation) but these have to be extracted from a sum over all such dynamic saddle-point processes. We propose a conjecture on how the different infinite-time solutions to the mean-field dynamical equations are related by a certain group of transformations. We then show that if all relevant saddle-points are obtained from Sompolinsky's solution through these transformations, the resulting P(q) is identical to that obtained with the Parisi scheme in replica space.