Oil-water interface in the Widom model: is it smooth, rough or crumpled?

The interface in the two-dimensional Ising model with only nearest-neighbour ferromagnetic interactions is known to be rough at all temperatures T>0. The Widom model for ternary microemulsions is, effectively, a spin-1/2 Ising model with, not only nearest-neighbour ferromagnetic interactions, but also specific farther-neighbour antiferromagnetic interactions. We investigate the effects of these farther-neighbour interactions in the Widom model on the roughening properties of the interface by carrying out Monte Carlo simulations