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

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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.

Original languageEnglish (US)
Article number65
JournalElectronic Communications in Probability
Volume26
DOIs
StatePublished - 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

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