Gibbs states of the Hopfield model with extensively many patterns.

DOI10.1007/BF02179395zbMath1081.82570MaRDI QIDQ1593223

Pierre Picco, Véronique Gayrard, Anton Bovier

Publication date: 16 January 2001

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

zbMATH Keywords

spin glassesHopfield modelself-averagingGibbs states

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Neural nets applied to problems in time-dependent statistical mechanics (82C32)

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Cites Work

• Exponential inequalities for sums of random vectors
• Gibbs states of the Hopfield model in the regime of perfect memory
• Large deviation principles for the Hopfield model and the Kac-Hopfield model
• The replica-symmetric solution without replica trick for the Hopfield model
• Rigorous results on the thermodynamics of the dilute Hopfield model
• The free energy of a class of Hopfield models
• Neural networks and physical systems with emergent collective computational abilities.
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