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One-dimensional DLR invariant measures are regular

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Abstract

A system of infinite spins in one dimension is considered. The interaction is given by a pair potential −J xySxSy, whereS x,S y are the spins at the sitesx,y∈ℤ andJ xy=J(|x−y|) whereJ(|x−y|) decreases asymptotically in an integrable way. The self-interaction makes the system superstable. It is proven that any invariant DLR measure for this system satisfies Ruelle's superstable estimates (regularity condition).

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Authors and Affiliations

  1. Istituto di Matematica, Università degli Studi dell' Aquila, I-67100, L'Aquila, Italy

    A. De Masi

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  1. A. De Masi
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Communicated by E. Lieb

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De Masi, A. One-dimensional DLR invariant measures are regular. Commun.Math. Phys. 67, 43–50 (1979). https://doi.org/10.1007/BF01223199

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  • DOI: https://doi.org/10.1007/BF01223199

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