On the GREM approximation of TAP free energies

2024/01/24 by Giulia Sebastiani, Sebastiani, Giulia, Marius A. Schmidt +1
Mathematics · Physics and Astronomy · #60G70 #60J80 #82B44 #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Mechanics and Entropy #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2401.13507

openalex publication_date 2024/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish both a Boltzmann-Gibbs principle and a Parisi formula for the limiting free energy of an abstract GREM (Generalized Random Energy Model) which provides an approximation of the TAP (Thouless-Anderson-Palmer) free energies associated to the Sherrington-Kirkpatrick (SK) model.

Related

• Contributions to Random Energy Models
• On a nonhierarchical generalization of the Perceptron GREM
• A quenched large deviation principle and a Parisi formula for a Perceptron version of the GREM
• On concavity of TAP free energy in the SK model
• Projected generalized free energies for non-equilibrium states