Open Access
November 2015 The free energy in a multi-species Sherrington–Kirkpatrick model
Dmitry Panchenko
Ann. Probab. 43(6): 3494-3513 (November 2015). DOI: 10.1214/14-AOP967


The authors of [Ann. Henri Poincaré 16 (2015) 691–708] introduced a multi-species version of the Sherrington–Kirkpatrick model and suggested the analogue of the Parisi formula for the free energy. Using a variant of Guerra’s replica symmetry breaking interpolation, they showed that, under certain assumption on the interactions, the formula gives an upper bound on the limit of the free energy. In this paper we prove that the bound is sharp. This is achieved by developing a new multi-species form of the Ghirlanda–Guerra identities and showing that they force the overlaps within species to be completely determined by the overlaps of the whole system.


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Dmitry Panchenko. "The free energy in a multi-species Sherrington–Kirkpatrick model." Ann. Probab. 43 (6) 3494 - 3513, November 2015.


Received: 1 February 2014; Revised: 1 August 2014; Published: November 2015
First available in Project Euclid: 11 December 2015

zbMATH: 1338.60237
MathSciNet: MR3433586
Digital Object Identifier: 10.1214/14-AOP967

Primary: 60G09 , 60K35 , 82B44

Keywords: Sherrington–Kirkpatrick model , Spin glasses

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.43 • No. 6 • November 2015
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