Capillary length of a planar interface from low temperatures to the critical point: An Isingd=2 strip

The correlation length controlling the long-range decay of the density-density correlation function in the direction parallel to the interface is computed exactly, for T≤${\mathit{T}}_{\mathit{c}}$, in the two-dimensional Ising M×∞ strip periodic in the long direction with a (+/-) boundary condition in the other direction which creates a planar strongly fluctuating interface. A crossover from long-range capillary-wave-like behavior to short-range bulk correlations above ${\mathit{T}}_{\mathit{c}}$, a new scaling function, and corrections to scaling at ${\mathit{T}}_{\mathit{c}}$ are found.