First order wetting of rough substrates and quantum unbinding

Replica and functional renormalization group methods show that, with short range substrate forces or in strong fluctuation regimes, wetting of a self-affine rough wall in 2D turns first-order as soon as the wall roughness exponent exceeds the anisotropy index of bulk interface fluctuations. Different thresholds apply with long range forces in mean field regimes. For bond-disordered bulk, fixed point stability suggests similar results, which ultimately rely on basic properties of quantum bound states with asymptotically power-law repulsive potentials.