Necessary and sufficient conditions for the ghs inequality with applications to analysis and probability

Richard S. Ellis; Charles M. Newman

doi:10.1090/S0002-9947-1978-0492131-8

Necessary and sufficient conditions for the ghs inequality with applications to analysis and probability

Richard S. Ellis, Charles M. Newman

Mathematics

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

Abstract

The GHS inequality is an important tool in the study of the Ising model of ferromagnetism (a model in equilibrium statistical mechanics) and in Euclidean quantum field theory. This paper derives necessary and sufficient conditions on an Ising spin system for the GHS inequality to be valid. Applications to convexity-preserving properties of certain differential equations and diffusion processes are given.

Original language	English (US)
Pages (from-to)	83-99
Number of pages	17
Journal	Transactions of the American Mathematical Society
Volume	237
DOIs	https://doi.org/10.1090/S0002-9947-1978-0492131-8
State	Published - Mar 1978

Keywords

Convex function
GHS inequality
Ising model
Parabolic partial differential equation

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-1978-0492131-8

Cite this

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title = "Necessary and sufficient conditions for the ghs inequality with applications to analysis and probability",

abstract = "The GHS inequality is an important tool in the study of the Ising model of ferromagnetism (a model in equilibrium statistical mechanics) and in Euclidean quantum field theory. This paper derives necessary and sufficient conditions on an Ising spin system for the GHS inequality to be valid. Applications to convexity-preserving properties of certain differential equations and diffusion processes are given.",

keywords = "Convex function, GHS inequality, Ising model, Parabolic partial differential equation",

author = "Ellis, {Richard S.} and Newman, {Charles M.}",

year = "1978",

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AU - Ellis, Richard S.

AU - Newman, Charles M.

PY - 1978/3

Y1 - 1978/3

N2 - The GHS inequality is an important tool in the study of the Ising model of ferromagnetism (a model in equilibrium statistical mechanics) and in Euclidean quantum field theory. This paper derives necessary and sufficient conditions on an Ising spin system for the GHS inequality to be valid. Applications to convexity-preserving properties of certain differential equations and diffusion processes are given.

AB - The GHS inequality is an important tool in the study of the Ising model of ferromagnetism (a model in equilibrium statistical mechanics) and in Euclidean quantum field theory. This paper derives necessary and sufficient conditions on an Ising spin system for the GHS inequality to be valid. Applications to convexity-preserving properties of certain differential equations and diffusion processes are given.

KW - Convex function

KW - GHS inequality

KW - Ising model

KW - Parabolic partial differential equation

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -

Necessary and sufficient conditions for the ghs inequality with applications to analysis and probability

Abstract

Keywords

ASJC Scopus subject areas

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