Large deviations, Guerra's and A.S.S. Schemes, and the Parisi hypothesis

DOI10.1007/s10955-006-9108-9zbMath1133.82330OpenAlexW2069578851MaRDI QIDQ885030

Michel Talagrand

Publication date: 7 June 2007

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-006-9108-9

zbMATH Keywords

spin glassesmean field modelsParisi solution

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Large deviations (60F10)

Related Items

The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results, Equilibrium and dynamics of a multi-bath Sherrington–Kirkpatrick model, A multi-scale spin-glass mean-field model, Ultrametricity in spin glasses, Approximate Ultrametricity for Random Measures and Applications to Spin Glasses, The Replica Trick in the Frame of Replica Interpolation, Exponential control of overlap in the replica method for \(p\)-spin Sherrington-Kirkpatrick model, Cavity method in the spherical SK model, Variational bounds for the generalized random energy model, On the irrelevant disorder regime of pinning models, The emergence of the order parameter in the interpolating replica trick for disordered statistical mechanics systems

Cites Work

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• The Parisi formula
• General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity
• Quadratic replica coupling in the Sherrington–Kirkpatrick mean field spin glass model