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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Necessary and sufficient conditions for the $ {\rm GHS}$ inequality with applications to analysis and probability


Authors: Richard S. Ellis and Charles M. Newman
Journal: Trans. Amer. Math. Soc. 237 (1978), 83-99
MSC: Primary 26A84; Secondary 35K99, 60J99, 82.60
MathSciNet review: 0492131
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0492131-8
PII: S 0002-9947(1978)0492131-8
Keywords: GHS inequality, Ising model, convex function, parabolic partial differential equation
Article copyright: © Copyright 1978 American Mathematical Society