Local energy statistics in disordered systems: a proof of the local REM conjecture

TL;DR

This paper proves the local REM conjecture for certain disordered spin systems, showing that their local energy statistics match the random energy model under specific conditions.

Contribution

It provides necessary conditions for the local REM conjecture and demonstrates its validity in broad classes of spin glass models.

Findings

The local REM conjecture holds for short range spin glasses.

It also applies to mean field SK-type spin glasses.

Conditions are identified under which energy levels growing with system size are included.

Abstract

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 hold 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.