Triangular lattice solution for filling in a wedge

We give new analytical and numerical results for the wetting and filling problems in the triangular lattice Ising ferromagnet. Both the surface tension in the bulk and the wall free energy in the presence of a surface field are obtained exactly using the transfer matrix method. We use a thermodynamic argument to obtain the exact condition for the filling transition and perform Monte Carlo simulations to verify the applicability of this argument.