ZEROS OF THE TRIANGULAR POTTS-MODEL PARTITION-FUNCTION - A CONJECTURED DISTRIBUTION

We consider the q-state Potts model on the triangular lattice with two- and three-site interactions in alternate triangular faces, and determine zeroes of the partition function numerically in the case of pure three-site interactions. On the basis of a rigorous reciprocal symmetry and results on the zeroes for finite lattices, we conjecture that zeroes of the partition function of the triangular Potts model with pure three-site interactions in alternate triangular faces lie on a circle and a segment of the negative real axis. It is shown that the conjecture holds for q = 2, and that it reproduces the known critical point for general q, including the q = 1 site percolation.