A dynamical theory for the Potts, model, recently introduced by the author, is applied to the two-dimensional, nearest-neighbour system. A decimation procedure is defined and, in the leading order of the approximations involved, the critical dynamical exponent is obtained for different numbers of Potts states.
The Legendre transformation, a modification of the decimation method used in the real space renormalisation group, is employed to study the critical behaviour of the two-dimensional S-state Potts model which exhibits a second-order phase transition for S<or=4. Thermal and magnetic critical exponents are calculated for the percolation (S to 1), Ising (S=2) and three- and four-state Potts models. Decimation estimates of the critical exponents and critical points for S=2, 3 and 4 are also presented.