WIAS Preprint No. 269, (1996)

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.

Appeared in

  • Comm. Math. Phys., 187 (1997), pp. 523-566

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