The critical exponents of crystalline random surfaces Original Research Article

We report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to 642 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 642 lattice with a χ2 per degree of freedom of 1.7 although the best direct fit to the specific heat data yields a much lower value of a. We have measured the normal-normal correlation function in the crumpled phase and find that, within the accuracy of our simulations, the data can be described by a super-renormalizable field theory.