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Upper Bound on the Decay of Correlations in a General Class of O(N)-Symmetric Models

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Abstract

We consider a general class of two-dimensional spin systems, with continuous but not necessarily smooth, possibly long-range, O(N)-symmetric interactions, for which we establish algebraically decaying upper bounds on spin-spin correlations under all infinite-volume Gibbs measures.

As a by-product, we also obtain estimates on the effective resistance of a (possibly long-range) resistor network in which randomly selected edges are shorted.

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Authors and Affiliations

  1. Section de mathématiques, Université de Genève, Geneva, Switzerland

    Maxime Gagnebin & Yvan Velenik

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  1. Maxime Gagnebin
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  2. Yvan Velenik
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Correspondence to Yvan Velenik.

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Communicated by H. Spohn

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Gagnebin, M., Velenik, Y. Upper Bound on the Decay of Correlations in a General Class of O(N)-Symmetric Models. Commun. Math. Phys. 332, 1235–1255 (2014). https://doi.org/10.1007/s00220-014-2075-0

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  • DOI: https://doi.org/10.1007/s00220-014-2075-0

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