The Parisi Formula has a Unique Minimizer

In 1979, Parisi (Phys Rev Lett 43:1754–1756, 1979 ) 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 (Ann Math 163(1):221–263...

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Bibliographic Details
Published in:Communications in mathematical physics 2015-05, Vol.335 (3), p.1429-1444
Main Authors: Auffinger, Antonio, Chen, Wei-Kuo
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:In 1979, Parisi (Phys Rev Lett 43:1754–1756, 1979 ) 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 (Ann Math 163(1):221–263, 2006 ) and later generalized to the mixed p -spin models by Panchenko (Ann Probab 42(3):946–958, 2014 ). 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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-014-2254-z