Localisation-delocalisation transition in a solid-on-solid model with a pinning potential

The influence of pinning forces on domain-wall fluctuations is studied in a continuous planar solid-on-solid model with a one-dimensional interface. The system is simple enough so that exact results can be obtained for a variety of pinning forces. The pinning of the interface is formally equivalent to the binding of a quantum mechanical particle in a temperature-dependent effective potential. In the case of a short-range pinning force applied a finite distance from the edge of the system, there is a localisation-delocalisation transition at a finite temperature. The transition is qualitatively similar to that studied in the d=2 Ising model by O.B. Abraham (see Phys. Rev. Lett., vol.44, p.1165-8, 1980).