  We develop a new pressure representation theorem for nearest-neighbour Gibbs
interactions and apply this to obtain the existence of efficient algorithms for
approximating the pressure in the $2$-dimensional ferromagnetic Potts,
multi-type Widom-Rowlinson and hard-core models. For Potts, our results apply
to every inverse temperature but the critical. For Widom-Rowlinson and
hard-core, they apply to certain subsets of both the subcritical and
supercritical regions. The main novelty of our work is in the latter.
