Compactness and the maximal Gibbs state for random Gibbs fields on a lattice |
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Authors: | Jean Bellissard Raphael Høegh-Krohn |
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Institution: | (1) Université de Provence, and Centre de Physique Théorique, CNRS, Luminy, Case 907, F-13288 Marseille, Cedex 2, France;(2) Institute of Mathematics, University of Oslo, Oslo, Norway |
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Abstract: | We prove for a general class of Gibbsian Random Field on ![Zopf](/content/qg25237150845654/xxlarge8484.gif) that the set of tempered Gibbs states is compact. This class contains the Euclidean random fields. Moreover if the interaction is attractive, there is a unique minimal and maximal Gibbs state – and +× ± are unique translation invariant ant and have the global Markov property. We also prove that uniqueness of the tempered Gibbs state is equivalent to the magnetizationsm
±= ±(q
x
) being equal which is true if the pressure is differentiable. |
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Keywords: | |
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