## The Annals of Probability

### Free energy in the mixed $p$-spin models with vector spins

Dmitry Panchenko

#### 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.

#### Article information

Source
Ann. Probab., Volume 46, Number 2 (2018), 865-896.

Dates
Revised: April 2017
First available in Project Euclid: 9 March 2018

https://projecteuclid.org/euclid.aop/1520586271

Digital Object Identifier
doi:10.1214/17-AOP1194

Mathematical Reviews number (MathSciNet)
MR3773376

Zentralblatt MATH identifier
06864075

#### Citation

Panchenko, Dmitry. Free energy in the mixed $p$-spin models with vector spins. Ann. Probab. 46 (2018), no. 2, 865--896. doi:10.1214/17-AOP1194. https://projecteuclid.org/euclid.aop/1520586271

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