Comment on "Growth Inside a Corner: The Limiting Interface Shape"

TL;DR

This paper investigates the asymptotic shape of a 3D corner growth model by numerical simulations, finding results that challenge previous conjectures about its growth velocity and shape.

Contribution

It introduces a novel mapping to a restricted solid-on-solid model and provides high-precision numerical evidence against the existing conjecture.

Findings

Numerical results contradict the conjectured asymptotic shape.

Monte Carlo simulations yield precise growth velocity estimates.

The study refines understanding of the 3D corner growth model's behavior.

Abstract

We examine the conjectured asymptotic shape of the three dimensional corner growth model [Olejarz et. al.,PRL, 108, 016102 (2012)] by mapping the model onto a restricted solid on solid model on a triangular lattice. By choosing appropriate boundary conditions, we are able to obtain high precision numerical results for the growth velocity using Monte Carlo simulations. We find that the numerical results are not consistent with the conjecture.