Universal Behavior of the Equilibrium Crystal Shape near the Facet Edge. I. A Generalized Terrace-Step-Kink Model

Abstract

A generalized version of the terrace-step-kink (TSK) model is introduced to study in detail the shape of a crystal near the facet edge. The model is analyzed by the transfer-matrix method combined with the lattice fermion approach. As a result, behavior of the curvature near the facet edge is found to have unexpected new features: finite Gaussian curvature jump with universal amplitude and vanishing transverse curvature with universal exponent.