3D crystal: how flat its flat facets are?

TL;DR

This paper explores the flatness of facets in 3D Ising model crystals, proposing a weakened hypothesis and proving it for the Solid-On-Solid model, advancing understanding of crystal surface behavior.

Contribution

It introduces a weakened hypothesis about crystal facets and proves it within the Solid-On-Solid model, extending theoretical insights into crystal surface phenomena.

Findings

Weaker hypothesis about crystal facet flatness is valid for the Solid-On-Solid model.

Formation of an extra monolayer can affect facet flatness.

Theoretical proof supports the hypothesis in a specific lattice model.

Abstract

We investigate the hypothesis that the (random) crystal of the $(-)$-phase inside the $(+)$-phase of the 3D canonical Ising model has flat facets. We argue that it might need to be weakened, due to the possibility of formation of extra monolayer on a facet. We then prove this weaker hypothesis for the Solid-On-Solid model.