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Pinning of an interface by a weak potential. (English) Zbl 0925.82024

Summary: We prove that in a two-dimensional Gaussian SOS model with a small attractive potential the height of the interface remains bounded no matter how small the potential is; this is in sharp contrast with the free situation in which the interface height diverges logarithmically in the thermodynamic limit.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics
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