2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126744We present exact derivations of the effective capillary wave fluctuation induced forces resulting from pinning of an interface between two coexisting phases at two points separated by a distance r. In two dimensions the Ising ferromagnet calculations based on the transfer matrix approach give an attractive force decaying as 1/r for large distances. In three dimensions mapping of the body-centered solid-on-solid model onto the 6-vertex model allows for exact solution using the bosonization analysis of the equivalent XXZ Heisenberg quantum chain. The exact result gives the attractive force which decays asymptotically as 1/(r\log r).4 pages, 2 figures, accepted for publication in Phys. Rev. LettStatistical MechanicsSoft Condensed Mattertext