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Symmetries and correlation inequalities for classicaln-vector models

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Abstract

We describe a new class of single spin measures on then-dimensional sphereS nr of radiusr (n ⩽ 4) for which Lebowitz-type [J. Lebowitz,J. Stat. Phys. 16:463 (1977)] inequalities hold. This is achieved by an appropriate parametrization ofS nr . The above class includes the uniform measures onxs ε ℝRn ∶ρ ⩽ ¦x¦ ⩽r for any 0 ⩽νp ⩽ r. The second topic of this paper is an abstract formulation of the first Griffiths inequality [R. B. Griffiths,J. Math. Phys. 8:478 (1967)] and the underlying symmetry property.

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  1. Fakultät für Mathematik, Universität Bielefeld, UniversitätsstraBe 25, 4800, Bielefeld 1, Germany

    Norbert Kalus

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  1. Norbert Kalus
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Kalus, N. Symmetries and correlation inequalities for classicaln-vector models. J Stat Phys 25, 635–643 (1981). https://doi.org/10.1007/BF01022358

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