It is conjectured that the singularities in the free energy for the q-state Potts model on the square lattice lie on two self-dual circles in the complex x plane where x=exp(-J/kT) is the usual low-temperature variable. These circles are natural generalisations of the known circles for the Ising model (q=2). The conjecture leads to the prediction that there is a single antiferromagnetic critical point at x=1+(q/(q-1))12/.

John Ramshaw was working at Los Alamos Scientific Laboratory at the time of writing.