Open Access
2023 On the second moment method and RS phase of multi-species spherical spin glasses
Eliran Subag
Author Affiliations +
Electron. J. Probab. 28: 1-21 (2023). DOI: 10.1214/23-EJP933


Excluding some special cases, computing the critical inverse-temperature βc of a mixed p-spin spin glass model is a difficult task. The only known method to calculate its value for a general model requires the full power of the Parisi formula. On the other hand, an easy application of the second moment method to the partition function yields an explicit lower bound βmβc to the critical inverse-temperature. Interestingly, in the important case of the Sherrington-Kirkpatrick model βm=βc. In this work we consider the multi-species spherical mixed p-spin models without external field, and characterize by a simple condition the models for which the second moment method works in the whole replica symmetric phase, namely, models such that βm=βc. In particular, for those models we obtain the value of βc.

Funding Statement

This project has received funding from the Israel Science Foundation (Grant Agreement No. 2055/21).


The author is the incumbent of The Skirball Chair in New Scientists.


Download Citation

Eliran Subag. "On the second moment method and RS phase of multi-species spherical spin glasses." Electron. J. Probab. 28 1 - 21, 2023.


Received: 3 May 2022; Accepted: 13 March 2023; Published: 2023
First available in Project Euclid: 4 April 2023

arXiv: 2111.07133
MathSciNet: MR4570231
zbMATH: 1515.82157
Digital Object Identifier: 10.1214/23-EJP933

Primary: 60G15 , 60G60 , 82D30

Keywords: replica symmetry , second moment , Spin glasses

Vol.28 • 2023
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