Rigorous results on some simple spin glass models
- Bovier, Anton
- Kurkova, Irina
2010 Mathematics Subject Classification
- 82B44 60G70 60K35
- Gaussian processes, generalized random energy model, continuous hierarchies, spin glasses, Poisson cascades, probability cascades, Ghirlanda-Guerra identities
In this paper we review some recent rigorous results that provide an essentially complete solution of a class of spin glass models introduced by Derrida in the 1980ies. These models are based on Gaussian random processes on the N-dimensional hypercube whose covariance is a function of a ultrametric distance on that set. We prove the convergence of the free energy as well as the Gibbs measures in an appropriate sense. These results confirm fully the predictions of the replica method including in situations where continuous replica symmetry breaking takes place.
- Markov Proc. Rel. Fields, 9 (2003), pp.209-242