THE FREE-ENERGY OF THE POTTS-MODEL - FROM THE CONTINUOUS TO THE 1ST-ORDER TRANSITION REGION

We present a large-q expansion of the 2d q-states Potts model free energies up to order 9 in 1/square-root q. Its analysis leads us to an ansatz which, in the first-order region, incorporates properties inferred from the known critical regime at q = 4, and predicts, for q > 4, the n-th energy cumulant scales as the power (3n/2 - 2) of the correlation length. The parameter-free energy distributions reproduce accurately, without reference to any interface effect, the numerical data obtained in a simulation for q = 10 with lattices of linear dimensions up to L = 50. The pure-phase specific heats are predicted to be much larger, at q less-than-or-equal-to 10, than the values extracted from the current finite-size scaling analysis of the extrema. Implications for safe numerical determinations of interface tensions are discussed.