The Parisi Formula has a Unique Minimizer

Antonio Auffinger, Wei Kuo Chen*

*Corresponding author for this work

Research output: Contribution to journalArticle

31 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1429-1444
Number of pages16
JournalCommunications in Mathematical Physics
Volume335
Issue number3
DOIs
StatePublished - Jan 1 2015

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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