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March 2018 Free energy in the mixed $p$-spin models with vector spins
Dmitry Panchenko
Ann. Probab. 46(2): 865-896 (March 2018). DOI: 10.1214/17-AOP1194

Abstract

Using the synchronization mechanism developed in the previous work on the Potts spin glass model, we obtain the analogue of the Parisi formula for the free energy in the mixed even $p$-spin models with vector spins, which include the Sherrington–Kirkpatrick model with vector spins interacting through their scalar product. As a special case, this also establishes the sharpness of Talagrand’s upper bound for the free energy of multiple mixed $p$-spin systems coupled by constraining their overlaps.

Citation

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Dmitry Panchenko. "Free energy in the mixed $p$-spin models with vector spins." Ann. Probab. 46 (2) 865 - 896, March 2018. https://doi.org/10.1214/17-AOP1194

Information

Received: 1 April 2016; Revised: 1 April 2017; Published: March 2018
First available in Project Euclid: 9 March 2018

zbMATH: 06864075
MathSciNet: MR3773376
Digital Object Identifier: 10.1214/17-AOP1194

Subjects:
Primary: 60F10, 60G15, 60K35, 82B44

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 2 • March 2018
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