Universality of hypercubic random surfaces

TL;DR

This paper demonstrates that hypercubic random surfaces with and without local restrictions share the same universality class, characterized by an entropy exponent of 1/2, with differences mainly due to finite size effects.

Contribution

The study proves the universality of hypercubic random surfaces regardless of local restrictions, unifying previously thought separate classes.

Findings

Both models have entropy exponent gamma = 1/2.

Restricted and unrestricted models belong to the same universality class.

Finite size effects are more significant in the restricted model.

Abstract

We study universality properties of the Weingarten hyper-cubic random surfaces. Since a long time ago the model with a local restriction forbidding surface self-bendings has been thought to be in a different universality class from the unrestricted model defined on the full set of surfaces. We show that both models in fact belong to the same universality class with the entropy exponent gamma = 1/2 and differ by finite size effects which are much more pronounced in the restricted model.