On the Wulff construction as a problem of equivalence of statistical   ensembles
  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. 
Salvador Miracle-Sole and Jean Ruiz
cond-mat.stat-mech math-ph math.MP