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 $1/\sqrt{q}$. 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 $n^{\mathrm{th}}$ 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 $q\le 10$, than the values extracted from current finite size scaling analysis of extrema. Implications for safe numerical determinations of interface tensions are discussed.

Comments: 11 pages, plain tex with 3 Postscript figures included Postscript file available by anonymous ftp://amoco.saclay.cea.fr/pubs.spht/93-022.ps