Interpolation and Comparison Methods in the Mean Field Spin Glass Model

DOI10.1007/978-3-319-05254-0_1zbMath1329.82133OpenAlexW294568192MaRDI QIDQ2948970

Francesco Guerra

Publication date: 7 October 2015

Published in: Trends in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-05254-0_1

zbMATH Keywords

Parisi solutionbreaking of replica symmetrycomplex disordered systemsmean field Sherrington-Kirkpatrick formulation

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)

Related Items

The discrete random energy model and one step replica symmetry breaking, One step replica symmetry breaking and overlaps between two temperatures

Cites Work

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• Mean field dilute ferromagnet: High temperature and zero temperature behavior
• The mean field Ising model trough interpolating techniques
• The high temperature region of the Viana-Bray diluted spin glass model
• The generalized Parisi formula
• Replica symmetry breaking in short-range spin glasses: Theoretical foundations and numerical evidences
• Bounds for diluted mean-fields spin glass models
• The thermodynamic limit in mean field spin glass models
• Replica bounds for optimization problems and diluted spin systems
• Broken replica symmetry bounds in the mean field spin glass model
• Multi-species mean field spin glasses. Rigorous results
• The Parisi formula
• Equilibrium statistical mechanics of bipartite spin systems
• Finite-range spin glasses in the Kac limit: free energy and local observables
• Course 5 An introduction to mean field spin glas theory: Methods and results
• About the ergodic regime in the analogical Hopfield neural networks: Moments of the partition function
• General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity
• The Sherrington-Kirkpatrick Model
• Some comments on the connection between disordered long range spin glass models and their mean field version
• The replica symmetric approximation of the analogical neural network
• The free energy in a multi-species Sherrington-Kirkpatrick model