The free energy of the Potts model

Abstract

We present a large q expansion of the 2d q-states Potts model free energies up to order 10 in 1/ trq. 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 (3 n/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.