Directed Percolation with long-range interactions: modeling non-equilibrium wetting

It is argued that some phase--transitions observed in models of non-equilibrium wetting phenomena are related to contact processes with long-range interactions. This is investigated by introducing a model where the activation rate of a site at the edge of an inactive island of length $\ell$ is $1+a\ell^{-\sigma}$. Mean--field analysis and numerical simulations indicate that for $\sigma>1$ the transition is continuous and belongs to the universality class of directed percolation, while for $0<\sigma<1$, the transition becomes first order. This criterion is then applied to discuss critical properties of various models of non--equilibrium wetting.