Rigorous low-temperature results for the mean field \(p\)-spins interaction model

DOI10.1007/s004400000070zbMath1016.82021OpenAlexW2048205873MaRDI QIDQ1579891

Michel Talagrand

Publication date: 13 February 2003

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s004400000070

zbMATH Keywords

disordered systemsmean field spin glasses

Mathematics Subject Classification ID

Gaussian processes (60G15) Inequalities; stochastic orderings (60E15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) 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) Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (13)

Exponential inequalities and convergence of moments in the replica-symmetric regime of the Hopfield model. ⋮ Fluctuations of the free energy in the REM and the \(p\)-spin SK models ⋮ On Gaussian spin glass with P-wise interactions ⋮ On the distribution of the overlaps at given disorder ⋮ The free energy of spherical pure \(p\)-spin models: computation from the TAP approach ⋮ On the second moment method and RS phase of multi-species spherical spin glasses ⋮ Random subcubes as a toy model for constraint satisfaction problems ⋮ Two Spaces Looking for a Geometer ⋮ Moderate deviations for the overlap parameter in the Hopfield model ⋮ Construction of pure states in mean field models for spin glasses ⋮ Statistical mechanics methods and phase transitions in optimization problems ⋮ Rigorous results for mean field models for spin glasses ⋮ Ergodicity: How Can It Be Broken?

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