Electronic Journal of Probability

The Aizenman-Sims-Starr scheme and Parisi formula for mixed $p$-spin spherical models

Wei-Kuo Chen

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Abstract

The Parisi formula for the free energy in the spherical models with mixed even $p$-spin interactions was proven in Michel Talagrand. In this paper we study the general mixed $p$-spin spherical models including $p$-spin interactions for odd $p$. We establish the Aizenman Sims-Starr scheme and from this together with many well-known results and Dmitry Panchenko's recent proof on the Parisi ultrametricity conjecture, we prove the Parisi formula.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 94, 14 pp.

Dates
Accepted: 29 October 2013
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064319

Digital Object Identifier
doi:10.1214/EJP.v18-2580

Mathematical Reviews number (MathSciNet)
MR3126577

Zentralblatt MATH identifier
1288.60127

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Chen, Wei-Kuo. The Aizenman-Sims-Starr scheme and Parisi formula for mixed $p$-spin spherical models. Electron. J. Probab. 18 (2013), paper no. 94, 14 pp. doi:10.1214/EJP.v18-2580. https://projecteuclid.org/euclid.ejp/1465064319


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References

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