Fisher zeros of the Q - state Potts model in the complex temperature plane for nonzero external magnetic field

The microcanonical transfer matrix is used to study the distribution of the Fisher zeros of the Q > 2 Potts models in the complex temperature plane with nonzero external magnetic field Hq. Unlike the Ising model for Hq 6= 0 which has only a non-physical critical point (the Fisher edge singularity), the Q > 2 Potts models have physical critical points forHq < 0 as well as the Fisher edge singularities for Hq > 0. For Hq < 0 the cross-over of the Fisher zeros of the Q-state Potts model into those of the (Q− 1)-state Potts model is discussed, and the critical line of the three-state Potts ferromagnet is determined. For Hq > 0 we investigate the edge singularity for finite lattices and compare our results with high-field, low-temperature series expansion of Enting. For 3 ≤ Q ≤ 6 we find that the specific heat, magnetization, susceptibility, and the density of zeros diverge at the Fisher edge singularity with exponents αe, βe, and γe which satisfy the scaling law αe + 2βe + γe = 2. Typeset using REVTEX ∗Electronic address: [email protected] †Electronic address: [email protected] 1