A model of random surfaces with non-trivial critical behaviour

Abstract We study a model of planar random surfaces based on gaussian imbedding of simplicial lattices in a D -dimensional space. The model is shown to be equivalent to a planar π 3 theory with exponential renormalized propagator for any dimension D . Scaling laws are derived and estimates for the exponents γ and ν by strong coupling expansions are obtained. The results differ from the predictions of mean field theory. γ depends on D and is probably zero for D = 4. The Hausdorff dimension is large (greater than four) but finite. The correlation length diverges at the critical point and the two-point function does not correspond to a free field theory. In general hyperscaling is not satisfied in such models.

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