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

In this note, 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, first established in Ref. 5. Published in On Three Levels: Micro, Meso and Macroscopic Approaches in Physics, M. Fannes and A. Verbeure (Eds.), Plenum Press, New York, 1994, pp. 295–302.