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.


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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