Some positive definite functions on sets and their application to the Ising model

Ole J. Heilmann, Daniel J. Kleitman, Elliott Lieb, Seymour Sherman

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Consideration of correlation inequalities for Ising ferromagnets with arbitrary spins has led to the discovery of a class of positive definite functions on sets. These functions are linear combinations of the functions which enter into Muirhead's Theorem. We prove these functions to be positive definite and also show how they can be applied to the Ising problem to prove Griffiths second inequality for arbitrary spins.

Original languageEnglish (US)
Pages (from-to)19-27
Number of pages9
JournalDiscrete Mathematics
Volume1
Issue number1
DOIs
StatePublished - Jan 1 1971

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Positive Definite Functions
Ising model
Ising Model
Ising
Correlation Inequalities
Ferromagnet
Arbitrary
Positive definite
Linear Combination
Theorem

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

Heilmann, Ole J. ; Kleitman, Daniel J. ; Lieb, Elliott ; Sherman, Seymour. / Some positive definite functions on sets and their application to the Ising model. In: Discrete Mathematics. 1971 ; Vol. 1, No. 1. pp. 19-27.
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Some positive definite functions on sets and their application to the Ising model. / Heilmann, Ole J.; Kleitman, Daniel J.; Lieb, Elliott; Sherman, Seymour.

In: Discrete Mathematics, Vol. 1, No. 1, 01.01.1971, p. 19-27.

Research output: Contribution to journalArticle

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