On the Wulff construction as a problem of equivalence of statistical ensembles

TL;DR

This paper proves the validity of the Wulff construction for 1D SOS models with a fixed area constraint by establishing thermodynamic limits and ensemble equivalence, providing a microscopic proof of the shape formation principle.

Contribution

It offers a new microscopic proof of the Wulff construction's validity for constrained SOS models, demonstrating ensemble equivalence and thermodynamic limit existence.

Findings

Existence of thermodynamic limits for the models

Equivalence of statistical ensembles established

Validation of the Wulff construction for these models

Abstract

The statistical mechanics of SOS (solid-on-solid) 1-dimensional models under the global constraint of having a specified area between the interface and the horizontal axis, is studied. We prove the existence of the thermodynamic limits and the equivalence of the corresponding statistical mechanics. This gives a simple alternative microscopic proof of the validity of the Wulff construction for such models.