The Annals of Probability

The free energy in a multi-species Sherrington–Kirkpatrick model

Dmitry Panchenko

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Abstract

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.

Article information

Source
Ann. Probab., Volume 43, Number 6 (2015), 3494-3513.

Dates
Received: February 2014
Revised: August 2014
First available in Project Euclid: 11 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.aop/1449843635

Digital Object Identifier
doi:10.1214/14-AOP967

Mathematical Reviews number (MathSciNet)
MR3433586

Zentralblatt MATH identifier
1338.60237

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G09: Exchangeability 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)

Keywords
Spin glasses Sherrington–Kirkpatrick model

Citation

Panchenko, Dmitry. The free energy in a multi-species Sherrington–Kirkpatrick model. Ann. Probab. 43 (2015), no. 6, 3494--3513. doi:10.1214/14-AOP967. https://projecteuclid.org/euclid.aop/1449843635


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References

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