FREE ENERGY OF A DILUTED SPIN GLASS MODEL WITH QUADRATIC HAMILTONIAN

Ratul Biswas; Wei Kuo Chen; Arnab Sen

doi:10.1214/22-AOP1597

FREE ENERGY OF A DILUTED SPIN GLASS MODEL WITH QUADRATIC HAMILTONIAN

Ratul Biswas
, Wei Kuo Chen
, Arnab Sen

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English (US)
Pages (from-to)	359-395
Number of pages	37
Journal	Annals of Probability
Volume	51
Issue number	1
DOIs	https://doi.org/10.1214/22-AOP1597
State	Published - 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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10.1214/22-AOP1597

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title = "FREE ENERGY OF A DILUTED SPIN GLASS MODEL WITH QUADRATIC HAMILTONIAN",

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.",

keywords = "Diluted model, Gardner problem, Shcherbina–tirozzi model.",

author = "Ratul Biswas and Chen, \{Wei Kuo\} and Arnab Sen",

note = "Funding Information: R. B. and W.-K. C. were partly supported by NSF Career Grant DMS 1752184. Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2023",

year = "2023",

doi = "10.1214/22-AOP1597",

language = "English (US)",

volume = "51",

pages = "359--395",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

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TY - JOUR

T1 - FREE ENERGY OF A DILUTED SPIN GLASS MODEL WITH QUADRATIC HAMILTONIAN

AU - Biswas, Ratul

AU - Chen, Wei Kuo

AU - Sen, Arnab

N1 - Funding Information: R. B. and W.-K. C. were partly supported by NSF Career Grant DMS 1752184. Publisher Copyright: © Institute of Mathematical Statistics, 2023

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Diluted model

KW - Gardner problem

KW - Shcherbina–tirozzi model.

UR - https://www.scopus.com/pages/publications/85143751791

UR - https://www.scopus.com/pages/publications/85143751791#tab=citedBy

U2 - 10.1214/22-AOP1597

DO - 10.1214/22-AOP1597

M3 - Article

AN - SCOPUS:85143751791

SN - 0091-1798

VL - 51

SP - 359

EP - 395

JO - Annals of Probability

JF - Annals of Probability

IS - 1

ER -

FREE ENERGY OF A DILUTED SPIN GLASS MODEL WITH QUADRATIC HAMILTONIAN

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