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 $ν=0.71(5)$ from the tangent-tangent correlation function whereas we find $ν=0.73(6)$ by assuming finite size scaling of the specific heat peak and hyperscaling. These results imply a specific heat exponent $α=0.58(10)$; this is a good fit to the specific heat on a $64^2$ lattice with a $χ^2$ per degree of freedom of 1.7 although the best direct fit to the specific heat data yields a much lower value of $α$. 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.