Universality of hypercubic random surfaces

We study universality properties of the Weingarten hyper-cubic random surfaces. Since a long time the model of hypercubic random surfaces with a local restriction forbidding surface self-bendings was thought to be in a different universality class from the unrestricted model defined on the full set of surfaces. In this paper we show that both models in fact belong to the same universality class with the entropy exponent γ = 12 and differ by the finite size effects which are much more pronounced in the restricted model.