  Interfacial structure and correlation functions near a two-dimensional (2D)
wedge filling transition are studied using effective interfacial Hamiltonian
models. An exact solution for short range binding potentials and results for
Kratzer binding potentials show that sufficiently close to the filling
transition a new length scale emerges and controls the decay of the interfacial
profile relative to the substrate and the correlations between interfacial
positions above different positions. This new length scale is much larger than
the intrinsic interfacial correlation length, and it is related geometrically
to the average value of the interfacial position above the wedge midpoint. The
interfacial behavior is consistent with a breather mode fluctuation picture,
which is shown to emerge from an exact decimation functional renormalization
group scheme that keeps the geometry invariant.
