  We present results of a microscopic density functional theory study of wedge
filling transitions, at a right-angle wedge, in the presence of dispersion-like
wall-fluid forces. Far from the corner the walls of the wedge show a
first-order wetting transition at a temperature $T_w$ which is progressively
closer to the bulk critical temperature $T_c$ as the strength of the wall
forces is reduced. In addition, the meniscus formed near the corner undergoes a
filling transition at a temperature $T_f<T_w$, the value of which is found to
be in excellent agreement with macroscopic predictions. We show that the
filling transition is {\it first-order} if it occurs far from the critical
point but is {\it continuous} if $T_f$ is close to $T_c$ even though the walls
still show first-order wetting behaviour. For this continuous transition the
distance of the meniscus from the apex grows as $\ell_w\approx
(T_f-T)^{-\beta_w}$ with critical exponent $\beta_w\approx 0.46 \pm 0.05$ in
good agreement with the phenomenological effective Hamiltonian prediction. Our
results suggest that critical filling transitions, with accompanying large
scale universal interfacial fluctuation effects, are more generic than thought
previously, and are experimentally accessible.
