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Extended universality of the surface curvature in equilibrium crystal shapes

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN: 1063-651X, Vol: 56, Issue: 1, Page: 355-362
1997
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Article Description

We investigate the universal property of curvatures in surface models that 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 restricted solid-on-solid 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 a clear understanding of the universal curvature jump at roughening transitions and facet edges and also provides an efficient way of locating the phase boundaries. © 1997 The American Physical Society.

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