Magnetization profiles of the planar fluctuating interface in ad=2 Ising strip

Transfer-matrix solution of the d=2 infinite Ising strip with fixed boundary conditions [D. B. Abraham and A. Martin-Löf, Commun. Math. Phys. 39, 245 (1973)] is adapted to the particular case of the (+/-) boundary. The soft mode of the fluctuating interface is studied at all temperatures T<${\mathit{T}}_{\mathit{c}}$ and beyond ${\mathit{T}}_{\mathit{c}}$ thus generalizing the capillary-wave and solid-on-solid (SOS) results to a system with bulk density fluctuations. In this paper the density or magnetization profile m(z) and its width W are calculated for a wide range of the strip length M perpendicular to the interface. The transition of the density profile from the low-temperature SOS regime through the critical region to the homogeneous one-phase system is described in detail and the scaling of m(z,T,M) and of W(T,M) is found.