The Roughening Transition in Surface Models with Non-Local Potentials.

The high temperature behavior of a class of surface models with exponentially decaying non-local potentials is studied. The existence of a phase in which fluctuations in the interface described by the model grow logarithmically with the separation between the points of observation is proved. Since these models presumably possess a low temperature phase with uniformly bounded fluctuations, this establishes the occurrence of a roughening transition for these models. The possible extension of these results to models of surfaces with overhangs is briefly discussed. Both upper and lower bounds on the fluctuations of the surface are derived. The upper bound combines a Mayer expansion with a duality transformation to rewrite the model as a spin system whose correlations may be bounded by complex translations. The lower bound combines a Mayer expansion with renormalization group ideas.