SINGULAR BEHAVIOR OF THE POTTS-MODEL IN THE THERMODYNAMIC LIMIT

The self-duality transformation is applied to the Fisher zeroes near t he critical point in the thermodynamic limit in the q > 4 state Potts model in two dimensions. A requirement that the locus of the duals of the zeroes be identical to the dual of the locus of zeroes (i) recover s the ratio of specific heat to internal energy discontinuity at criti cality and the relationships between the discontinuities of higher cum ulants and (ii) identifies duality with complex conjugation. Conjectur ing that all zeroes governing ferromagnetic critical behaviour satisfy the latter requirement, the full locus of Fisher zeroes is shown to b e a circle. This locus, together with the density of zeroes is shown t o be sufficient to recover the singular form of all thermodynamic func tions in the thermodynamic limit.