FREE ENERGY OF A DILUTED SPIN GLASS MODEL WITH QUADRATIC HAMILTONIAN

Ratul Biswas, Wei Kuo Chen, Arnab Sen

Research output: Contribution to journalArticlepeer-review

Abstract

We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of the spins in the system with varying edge connectivity. The key ingredient in our argument is played by the identification of these random variables as the unique solution to a recursive distributional equation. Our results in particular provide the first example of the diluted Shcherbina–Tirozzi model, whose limiting free energy can be derived at any inverse temperature and external field.

Original languageEnglish (US)
Pages (from-to)359-395
Number of pages37
JournalAnnals of Probability
Volume51
Issue number1
DOIs
StatePublished - 2023

Bibliographical note

Funding Information:
R. B. and W.-K. C. were partly supported by NSF Career Grant DMS 1752184.

Publisher Copyright:
© Institute of Mathematical Statistics, 2023

Keywords

  • Diluted model
  • Gardner problem
  • Shcherbina–tirozzi model.

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