The phase transition of the pure Potts model is indeed first-order for q≥5 but a continuous transition is induced for any number of states q when the exchange couplings are made random. In the large q-limit, the central charge has been conjectured to follow the law
c(q)=12ln2q
See the reference J.L. Jacobsen, and M. Picco (2000), Phys. Rev. E 61, R13. Note that there are some subtleties in the definition of c. The precise CFT of the random Potts model is not known but it cannot be unitary.