Winterbottom Construction for Finite Range Ferromagnetic Models: An L_1 Approach

Abstract

We provide a rigorous microscopic derivation of the thermodynamic description of equilibrium crystal shapes in the presence of a substrate, first studied by Winterbottom. We consider finite range ferromagnetic Ising models with pair interactions in dimensions greater or equal to 3, and model the substrate by a finite-range boundary magnetic field acting on the spins close to the bottom wall of the box.

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