Temperature Dependence of Facet Ridges in Crystal Surfaces

TL;DR

This study numerically investigates how temperature affects facet ridge endpoints in crystal surfaces modeled by a BCSOS system, revealing complex phase behaviors and anisotropic scaling at critical points.

Contribution

It introduces a detailed numerical analysis of facet ridge endpoints in a BCSOS model, highlighting temperature-dependent phase transitions and anisotropic critical scaling.

Findings

Ridge lines extend into the rough phase with surface orientation jumps.

Rough-to-faceted edges are first-order with orientation jumps.

Critical endpoints exhibit anisotropic scaling with exponent z=3.

Abstract

The equilibrium crystal shape of a body-centered solid-on-solid (BCSOS) model on a honeycomb lattice is studied numerically. We focus on the facet ridge endpoints (FRE). These points are equivalent to one dimensional KPZ-type growth in the exactly soluble square lattice BCSOS model. In our more general context the transfer matrix is not stochastic at the FRE points, and a more complex structure develops. We observe ridge lines sticking into the rough phase where thesurface orientation jumps inside the rounded part of the crystal. Moreover, the rough-to-faceted edges become first-order with a jump in surface orientation, between the FRE point and Pokrovsky-Talapov (PT) type critical endpoints. The latter display anisotropic scaling with exponent $z=3$ instead of familiar PT value $z=2$.