Construction of pure states in mean field models for spin glasses
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Publication:707607
DOI10.1007/s00440-009-0242-6zbMath1204.82037OpenAlexW2087113927MaRDI QIDQ707607
Publication date: 8 October 2010
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00440-009-0242-6
Gaussian processes (60G15) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)
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Cites Work
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- The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results
- Free energy of the spherical mean field model
- Rigorous construction of the pure states for certain spin glass models
- Competing particle systems and the Ghirlanda-Guerra identities
- Derrida's generalised random energy models. I: Models with finitely many hierarchies
- Rigorous low-temperature results for the mean field \(p\)-spins interaction model
- On the stability of the quenched state in mean-field spin-glass models
- On the distribution of the overlaps at given disorder
- A connection between the Ghirlanda-Guerra identities and ultrametricity
- On the structure of quasi-stationary competing particle systems
- Parisi measures
- A question about the Parisi functional
- The Parisi formula
- General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity
- Rigorous results for mean field models for spin glasses