Harmonic Crystal on the Wall: A Microscopic Approach
A three dimensional Winterbottom type construction in the regime of partial wetting is derived in a scaling limit of a gas of microscopic Gaussian SOS droplets under the fixed volume constraint. The proof is based on a coarse graining of the random microscopic region “wetted” by the crystal, random walk representations of various quantities related to free massless fields and a stability analysis of the torsional rigidity problem.
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