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Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures

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Abstract

We give a condition on a Gibbs measure for an attractive Markov specification, which assures extremality and the global Markov property. As an example of application we consider the class of attractive Markov specifications defined on a compact configuration space over a two-dimensional lattice by the interaction Hamiltonians (assumed to have a finite set of periodic ground configurations) satisfying Peierl's condition. We prove that each extremal Gibbs measure for such a specification, at sufficiently low temperature, has the global Markov property.

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Authors and Affiliations

  1. Research Center Bielefeld-Bochum-Stochastics, Bielefeld University, D-4800, Bielefeld 1, Germany

    Boguslaw Zegarliński

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  1. Boguslaw Zegarliński
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On leave of absence from the Institute of Theoretical Physics, University of Wrocław, Poland.

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Zegarliński, B. Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures. J Stat Phys 43, 687–705 (1986). https://doi.org/10.1007/BF01020660

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  • DOI: https://doi.org/10.1007/BF01020660

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