Local energy statistics in disordered systems: a proof of the local REM conjecture. (English) Zbl 1104.82026
Summary: Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should, in most circumstances, be the same as in the random energy model. Here we give necessary conditions for this hypothesis to be true, which we show to be satisfied in wide classes of examples: short range spin glasses and mean field spin glasses of the SK type. We also show that, under certain conditions, the conjecture holds even if energy levels that grow moderately with the volume of the system are considered.
MSC:
| 82B44 | Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics |
Keywords:
spin glasses; random energy model; Sherrington-Kirkpatrick models; Ising models; Poisson point processReferences:
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