Energy statistics in disordered systems: The local REM conjecture and beyond

Details Energy statistics in disordered systems: The local REM conjecture and beyond Energy statistics in disordered systems: The local REM conjecture and beyond

2005-06-21

arxiv.org/abs/cond-mat/0506521v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

to appear in Proceedings of Applications of random matrices to economics and other complex systems

Scientific paper

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. In the case of the Generalised Random energy model, we give a complete analysis for the behaviour of the local energy statistics at all energy scales. In particular, we show that, in this case, the REM conjecture holds exactly up to energies $E_N<\b_c N$, where $\b_c$ is the critical temperature. We also explain the more complex behaviour that sets in at higher energies.

Affiliated with

Also associated with

No associations

Rating

Energy statistics in disordered systems: The local REM conjecture and beyond does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Energy statistics in disordered systems: The local REM conjecture and beyond, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Energy statistics in disordered systems: The local REM conjecture and beyond will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-292925