Cluster derivation of Parisi's RSB solution for disordered systems

Abstract

We propose a general scheme in which disordered systems are allowed to\nsacrifice energy equi-partitioning and separate into a hierarchy of ergodic\nsub-systems (clusters) with different characteristic time-scales and\ntemperatures. The details of the break-up follow from the requirement of\nstationarity of the entropy of the slower cluster, at every level in the\nhierarchy. We apply our ideas to the Sherrington-Kirkpatrick model, and show\nhow the Parisi solution can be {\\it derived} quantitatively from plausible\nphysical principles. Our approach gives new insight into the physics behind\nParisi's solution and its relations with other theories, numerical experiments,\nand short range models.\n