Authors: Christof Külske Frank Redig
Publish Date: 2005/09/12
Volume: 135, Issue: 3, Pages: 428-456
Abstract
For `high temperature initial measures we prove that the timeevoved 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 discretespin Gibbs measures there is no recovery of the Gibbs property for large t in the presence of a nonvanishing external magnetic field All of our results hold for any dimension d≥2 This example suggests more generally that timeevolved continuousspin models tend to be nonGibbsian more easily than their discretespin counterparts
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