The SK model is infinite step replica symmetry breaking at zero temperature
Preprint
Abstract
We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.Keywords
All Related Versions
This publication has 30 references indexed in Scilit:
- Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature: The Perturbative RegimeCommunications on Pure and Applied Mathematics, 2019
- Existence of Two-Step Replica Symmetry Breaking for the Spherical Mixed p-Spin Glass at Zero TemperatureCommunications in Mathematical Physics, 2018
- Optimization on sparse random hypergraphs and spin glassesRandom Structures & Algorithms, 2018
- Low Temperature Asymptotics of Spherical Mean Field Spin GlassesCommunications in Mathematical Physics, 2017
- The Legendre Structure of the Parisi FormulaCommunications in Mathematical Physics, 2016
- The Parisi Formula has a Unique MinimizerCommunications in Mathematical Physics, 2014
- Random Matrices and Complexity of Spin GlassesCommunications on Pure and Applied Mathematics, 2012
- The Parisi Formula2011
- Broken Replica Symmetry Bounds in the Mean Field Spin Glass ModelCommunications in Mathematical Physics, 2003
- Some rigorous results on the Sherrington-Kirkpatrick spin glass modelCommunications in Mathematical Physics, 1987