Extended variational principle for the Sherrington-Kirkpatrick spin-glass model

Michael Aizenman, Robert J Sims, Shannon L. Starr

Research output: Contribution to journalArticle

88 Citations (Scopus)

Abstract

The recent proof by Guerra that the Parisi ansatz provides a lower bound on the free energy of the Sherrington-Kirkpatrick (SK) spin-glass model could have been taken as offering some support to the validity of the purported solution. In this work we present a broader variational principle, in which the lower bound as well as the actual value are expressed through an optimization procedure for which ultrametric/hierarchal structures form only a subset of the variational class. The validity of Parisi's ansatz for the SK model is still in question. The new variational principle may be of help in critical review of the issue.

Original languageEnglish (US)
Article number214403
Pages (from-to)2144031-2144034
Number of pages4
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume68
Issue number21
StatePublished - Dec 2003
Externally publishedYes

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Spin glass
variational principles
spin glass
Free energy
set theory
free energy
optimization

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Extended variational principle for the Sherrington-Kirkpatrick spin-glass model. / Aizenman, Michael; Sims, Robert J; Starr, Shannon L.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 68, No. 21, 214403, 12.2003, p. 2144031-2144034.

Research output: Contribution to journalArticle

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