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

Ole J. Heilmann; Daniel J. Kleitman; Elliott H. Lieb; Seymour Sherman

doi:10.1016/0012-365X(71)90004-5

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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Pages (from-to)	19-27
Number of pages	9
Journal	Discrete Mathematics
Volume	1
Issue number	1
DOIs	https://doi.org/10.1016/0012-365X(71)90004-5
State	Published - May 1971

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(71)90004-5

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@article{08ac805a211f4c8f8745f585cc15a698,

title = "Some positive definite functions on sets and their application to the Ising model",

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.",

author = "Heilmann, {Ole J.} and Kleitman, {Daniel J.} and Lieb, {Elliott H.} and Seymour Sherman",

note = "Funding Information: $ On [cave from the Unrversrlt;! uf Copenhagen. Permanent address: Chemistry Lab. (Brsted Institute& Copenhagen, Denmark. + Work partially supported by National Science Foundation Grant GP-9414. ** Work supported by National Scicnze Foundation GP-I 3778. *{\textquoteleft}* Work partially supported b: National Suiencx Foundation Grant GP-7469.",

year = "1971",

month = may,

doi = "10.1016/0012-365X(71)90004-5",

language = "English (US)",

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pages = "19--27",

journal = "Discrete Mathematics",

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T1 - Some positive definite functions on sets and their application to the Ising model

AU - Heilmann, Ole J.

AU - Kleitman, Daniel J.

AU - Lieb, Elliott H.

AU - Sherman, Seymour

N1 - Funding Information: $ On [cave from the Unrversrlt;! uf Copenhagen. Permanent address: Chemistry Lab. (Brsted Institute& Copenhagen, Denmark. + Work partially supported by National Science Foundation Grant GP-9414. ** Work supported by National Scicnze Foundation GP-I 3778. *‘* Work partially supported b: National Suiencx Foundation Grant GP-7469.

PY - 1971/5

Y1 - 1971/5

N2 - 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.

AB - 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.

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U2 - 10.1016/0012-365X(71)90004-5

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EP - 27

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1

ER -

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

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