Analytical calculation of two leading exponents of the dilute Potts model

A Potts model on a square lattice with two- and four-spin interaction and site and bond dilution is shown to be dual to itself. The model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model. By means of these mappings the dilute Potts model can be written as a Gaussian-like model with staggered and direct periodic fields. The leading and next-to-leading exponents of the Potts model are calculated, subject to the validity of certain assumptions.