Extended Universality of the Surface Curvature in Equilibrium Crystal Shapes

TL;DR

This paper demonstrates the universal behavior of surface curvatures in equilibrium crystal shapes, linking the Hessian of free energy to Gaussian coupling, validated through theoretical and numerical methods.

Contribution

It generalizes a previously derived relation between free energy Hessian and Gaussian coupling to a broader setting using renormalization group analysis.

Findings

The Hessian relation holds in general settings.

Universal curvature jump at roughening transitions is explained.

Phase boundaries can be efficiently located using this relation.

Abstract

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.