The Critical Exponents of Crystalline Random Surfaces

Abstract

We report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to $64^2$ points. The critical exponents at the crumpling transition are determined by a number of methods all of which are shown to agree within estimated errors. The correlation length exponent is found to be $\nu =0.71(5)$ from the tangent-tangent correlation function whereas we find $\nu =0.73(6)$ by assuming finite size scaling of the specific heat peak and hyperscaling. These results imply a specific heat exponent $\alpha =0.58(10)$; this is a good fit to the specific heat on a $64^2$ lattice with a ${\chi }^2$ per degree of freedom of 1.7 although the best direct fit to the specific heat data yields a much lower value of $\alpha$. Our measurements of the normal-normal correlation functions suggest that the model in the crumpled phase is described by an effective field theory which deviates from a free field theory only by super-renormalizable interactions.

Comments: 18 pages standard LaTex with EPS figures