The Critical Exponents of Crystalline Random Surfaces

We report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to 64 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 tangenttangent 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 lattice with a χ 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. e-mail: [email protected]