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Fractal Failure of Quasilocality for a Majority Rule Transformation on a Tree

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Abstract

We provide a transformation of the Ising model on a Cayley tree leading to non-Gibbsianness at any temperature, i.e. even within the uniqueness regime. We also introduce a new type of pathologies of renormalized Gibbs measures, called the fractal failure of quasilocality, and exhibit a concrete example.

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Authors and Affiliations

  1. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France

    Arnaud Le Ny

  2. Analyse et modèles stochastiques, Université de Rouen, Site Colbert, 76821, Mont Saint Aignan Cedex, France

    Arnaud Le Ny

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  1. Arnaud Le Ny
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Ny, A.L. Fractal Failure of Quasilocality for a Majority Rule Transformation on a Tree. Letters in Mathematical Physics 54, 11–24 (2000). https://doi.org/10.1023/A:1007666725121

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  • DOI: https://doi.org/10.1023/A:1007666725121

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