On the replica symmetric equations for the Hopfield model

DOI10.1063/1.532935zbMath0988.82024OpenAlexW1970262190MaRDI QIDQ4270392

Mariya Shcherbina, Brunello Tirozzi, Leonid Pastur

Publication date: 21 November 1999

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

Full work available at URL: https://doi.org/10.1063/1.532935

zbMATH Keywords

disordered systemscentral limit theoremHopfield modelcavity fieldSherrington-KirkpatrickGibbs averagesreplica symmetric equations

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 (10)

Dreaming neural networks: rigorous results ⋮ Generalized Guerra's interpolation schemes for dense associative neural networks ⋮ Moderate deviations for the overlap parameter in the Hopfield model ⋮ The replica symmetric approximation of the analogical neural network ⋮ Spontaneous Replica Symmetry Breaking and Interpolation Methods for Complex Statistical Mechanics Systems ⋮ About the ergodic regime in the analogical Hopfield neural networks: Moments of the partition function ⋮ The relativistic Hopfield model with correlated patterns ⋮ Free energies of Boltzmann machines: self-averaging, annealed and replica symmetric approximations in the thermodynamic limit ⋮ On the volume of the intersection of a sphere with random half spaces ⋮ Replica symmetry breaking in neural networks: a few steps toward rigorous results

Cites Work

• Some rigorous results on the Sherrington-Kirkpatrick spin glass model.
• Fluctuation of the free energy in the Hopfield model
• The Sherrington-Kirkpatrick model: A challenge for mathematicians
• Rigorous results for the Hopfield model with many patterns
• The replica-symmetric solution without replica trick for the Hopfield model
• The free energy of a class of Hopfield models

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