X iv : h ep - t h / 93 03 07 5 v 1 1 2 M ar 1 99 3 The free energy of the Potts model : from the continuous to the first - order transition region

The free energy of the Potts model : from the continuous to the first-order transition region. ABSTRACT We present a large q expansion of the 2d q-states Potts model free energies up to order 9 in 1/ √ 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 ≤ 10, than the values extracted from current finite size scaling analysis of extrema. Implications for safe numerical determinations of interface tensions are discussed.