Exact solubility of the self-dual and the string melting points in the restricted solid-on-solid model

The restricted solid-on-solid model, which describes the roughening of two-dimensional interfaces, is found to be exactly soluble in two instances: at a point where the model is self-dual under the duality transformation of the five-state clock model and at the string melting transition where the model belongs to the same universality class as an Ising model on a transverse vibrating lattice. Both points are located in the subspace of the 19-vertex model solved by Zamolodchikov and Fateev (1980).