A Tomography of the GREM: Beyond the REM Conjecture
Copyright policy )A Tomography of the GREM: Beyond the REM Conjecture
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. This was proven in a large class of models for energies that do not grow too fast with the system size. Considering the example of the generalized random energy model, we show that the conjecture breaks down for energies proportional to the volume of the system, and describe the far more complex behavior that then sets in.
- French Institute for Research in Computer Science and Automation France
- New Sorbonne University France
- Weierstrass Institute Germany
- University of Paris France
- Leibniz Association Germany
ddc:510, [MATH.MATH-PR] Mathematics/Probability, spin glasses, extreme value theory, 60G70, level statistics -- random energy model -- generalized random energy model -- extreme value theory -- disordered systems -- spin glasses, article, generalized random energy model, FOS: Physical sciences, level statistics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 510, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], disordered systems, 82B45, random energy model, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
ddc:510, [MATH.MATH-PR] Mathematics/Probability, spin glasses, extreme value theory, 60G70, level statistics -- random energy model -- generalized random energy model -- extreme value theory -- disordered systems -- spin glasses, article, generalized random energy model, FOS: Physical sciences, level statistics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 510, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], disordered systems, 82B45, random energy model, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
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