Harmonic crystal on the wall: a microscopic approach
- Bolthausen, Erwin
- Ioffe, Dmitry
2010 Mathematics Subject Classification
- 60K35 82B24
- 2D Gaussian SOS model, Winterbottom construction, surface tension, random walk representation, torsional rigidity
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 representation of various quantities related to free massless fields and a stability analysis of the torsional rigidity problem.
- Comm. Math. Phys., 187 (1997), pp. 523-566