 06320 Christof Kuelske and Aernout C.D.van Enter
 Nonexistence of random gradient Gibbs measures in continuous interface models in d=2.
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Nov 7, 06

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Abstract. We consider statistical mechanics models of continuous spins in a disordered environment. These models have a natural interpretation as effective interface models. It is well known that without disorder there are no interface Gibbs measures in infinite volume in dimension d=2, while there are "gradient Gibbs measures", describing an infinitevolume distribution for the increments of the field, as was shown by Funaki and Spohn.
In the present paper we show that adding a disorder term prohibits the existence of such gradient Gibbs measures for general interaction potentials in d=2. This nonexistence result generalizes the simple case of Gaussian fields where it follows from an explicit computation.
In d=3, where random gradient Gibbs measures are expected to exist, our method provides a lower bound of the order of the inverse of the distance on the decay of correlations of Gibbs expectations w.r.t. the distribution of the random environment.
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