On the Crumpling Transition in Crystalline Random Surfaces

We investigate the crumpling transition on crystalline random surfaces with extrinsic curvature on lattices up to ${64}^2$. Our data are consistent with a second order phase transition and we find correlation length critical exponent $\nu =0.89\pm 0.07$. The specific heat exponent, $\alpha =0.2\pm 0.15$, is in much better agreement with hyperscaling than hitherto. The long distance behaviour of tangent-tangent correlation functions confirms that the so-called Hausdorff dimension is $d_H=\mathrm{\infty }$ throughout the crumpled phase.