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The Parisi formula has a unique minimizer

Antonio Auffinger Northwestern University Wei-Kuo Chen University of Minnesota

Probability mathscidoc:1704.28001

Gold Award Paper in 2017

Communications in Mathematical Physics, 335, (3), 1429-1444, 2015
In 1979, G. Parisi predicted a variational formula for the thermodynamic limit of the free energy in the Sherrington-Kirkpatrick model and described the role played by its minimizer. This formula was verified in the seminal work of Talagrand and later generalized to the mixed p-spin models by Panchenko. In this paper, we prove that the minimizer in Parisi's formula is unique at any temperature and external field by establishing the strict convexity of the Parisi functional.
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@inproceedings{antonio2015the,
  title={The Parisi formula has a unique minimizer},
  author={Antonio Auffinger, and Wei-Kuo Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170418214814332026741},
  booktitle={Communications in Mathematical Physics},
  volume={335},
  number={3},
  pages={1429-1444},
  year={2015},
}
Antonio Auffinger, and Wei-Kuo Chen. The Parisi formula has a unique minimizer. 2015. Vol. 335. In Communications in Mathematical Physics. pp.1429-1444. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170418214814332026741.
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