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Physical Review Letters

Griffiths' Theorems for the Ferromagnetic Heisenberg Model

C. A. Hurst, S. Sherman

Published Jun 23, 1969• 26 citations
Publisher

Abstract

It is shown that for the quantum mechanical Heisenberg ferromagnet, the correlation is not necessarily a monotone increasing function of interactions.Received 25 April 1969DOI:https://doi.org/10.1103/PhysRevLett.22.1357©1969 American Physical Society

DOI
10.1103/physrevlett.22.1357

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It is shown that for the quantum mechanical Heisenberg ferromagnet, the correlation is not necessarily a monotone increasing function of interactions.Received 25 April 1969DOI:https://doi.org/10.1103/PhysRevLett.22.1357©1969 American Physical Society
First, for a classical discrete approximation to the Heisenberg ferromagnet, in a Euclidean space of dimension 2k where k is a positive integer, the correlation is nonnegative and a monotonic increasing function of interactions. Second, for the quantum mechanical Heisenberg ferromagnet itself, the correlation is nonnegative but not necessarily a monotonic increasing function of interaction. Both results allow for long-range interactions. Third, a family of inequalities on the number of connected components in graphs is deduced.