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Title of Journal: Probab. Theory Relat. Fields

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Abbravation: Probability Theory and Related Fields

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Loss without recovery of Gibbsianness during diffusion of continuous spins

Authors: Christof Külske, Frank Redig,

Publish Date: 2005/09/12
Volume: 135, Issue:3, Pages: 428-456
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For `high temperature' initial measures we prove that the time-evoved measure μ t is Gibbsian for all t. For `low temperature' initial measures we prove that μ t stays Gibbsian for small enough times t, but loses its Gibbsian character for large enough t. In contrast to the analogous situation for discrete-spin Gibbs measures, there is no recovery of the Gibbs property for large t in the presence of a non-vanishing external magnetic field. All of our results hold for any dimension d≥2. This example suggests more generally that time-evolved continuous-spin models tend to be non-Gibbsian more easily than their discrete-spin counterparts.



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