Extended Universality of the Surface Curvature in Equilibrium Crystal Shapes

We investigate the universal property of curvatures in surface models which display a flat phase and a rough phase whose criticality is described by the Gaussian model. Earlier we derived a relation between the Hessian of the free energy and the Gaussian coupling constant in the six-vertex model. Here we show its validity in a general setting using renormalization group arguments. The general validity of the relation is confirmed numerically in the RSOS model by comparing the Hessian of the free energy and the Gaussian coupling constant in a transfer matrix finite-size-scaling study. The Hessian relation gives clear understanding of the universal curvature jump at roughening transitions and facet edges and also provides an efficient way of locating the phase boundaries.