Cluster derivation of Parisi's RSB solution for disordered systems

Details Cluster derivation of Parisi's RSB solution for disordered systems Cluster derivation of Parisi's RSB solution for disordered systems

2000-09-11

arxiv.org/abs/cond-mat/0009151v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages 5 figures

Scientific paper

10.1088/0305-4470/34/10/105

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 {\it 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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