Critical behaviour of the two-dimensional Potts model with a continuous number of states; A finite size scaling analysis

We investigate the critical behaviour of the two-dimensional, q-state Potts model, using finite-size scaling and transfer matrix methods. For the continuous transition range (0<q⩽4), we present accurate values of the thermal and magnetic exponents. These are in excellent agreement with the conjecture of den Nijs, and that of Nienhuis et al. and Pearson, respectively. Finite size scaling is extended for the description of the first order region (q>4). For completely finite systems, we recover the power law behaviour describe by discontinuity fixed point exponents; however, for systems that are infinite in one direction, exponential behaviour occurs. This is illustrated numerically by the exponential divergences of the susceptibility and specific heat with increasing system size for q⪢4.