On the almeida-thouless transition line in the sherrington-kirkpatrick model with centered gaussian external field*

Wei Kuo Chen

doi:10.1214/21-ECP439

On the almeida-thouless transition line in the sherrington-kirkpatrick model with centered gaussian external field^*

Wei Kuo Chen

School of Mathematics

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

1 Scopus citations

Abstract

We study the phase transition of the free energy in the Sherrington-Kirkpatrick mean-field spin glass model with centered Gaussian external field. We show that the corresponding Almeida-Thouless line is the correct transition curve that distinguishes between the replica symmetric and replica symmetry breaking solutions in the Parisi formula.

Original language	English (US)
Article number	65
Journal	Electronic Communications in Probability
Volume	26
DOIs	https://doi.org/10.1214/21-ECP439
State	Published - 2021

Bibliographical note

Funding Information:
*Partly supported by NSF grant DMS-17-52184. †University of Minnesota, United States of America. E-mail: wkchen@umn.edu

Publisher Copyright:
© 2021, Institute of Mathematical Statistics. All rights reserved.

Keywords

Almeida-Thouless line
Parisi formula
Sherrington-Kirkpatrick model

Publisher link

10.1214/21-ECP439

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abstract = "We study the phase transition of the free energy in the Sherrington-Kirkpatrick mean-field spin glass model with centered Gaussian external field. We show that the corresponding Almeida-Thouless line is the correct transition curve that distinguishes between the replica symmetric and replica symmetry breaking solutions in the Parisi formula.",

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N2 - We study the phase transition of the free energy in the Sherrington-Kirkpatrick mean-field spin glass model with centered Gaussian external field. We show that the corresponding Almeida-Thouless line is the correct transition curve that distinguishes between the replica symmetric and replica symmetry breaking solutions in the Parisi formula.

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KW - Parisi formula

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