Cluster derivation of Parisi's RSB solution for disordered systems
J. van Mourik, A. C. C. Coolen
Abstract
We propose a general scheme in which disordered systems are allowed to sacrifice energy equi-partitioning and separate into a hierarchy of ergodic sub-systems (clusters) with different characteristic time-scales and temperatures. The details of the break-up follow from the requirement of stationarity of the entropy of the slower cluster, at every level in the hierarchy. We apply our ideas to the Sherrington-Kirkpatrick model, and show how the Parisi solution can be derived quantitatively from plausible physical principles. Our approach gives new insight into the physics behind Parisi's solution and its relations with other theories, numerical experiments, and short range models.
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