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The properties of the partition function zeros in the complex temperature plane (Fisher zeros) and in the complex Q plane (Potts zeros) are investigated for the Q-state Potts model in an arbitrary nonzero external magnetic eld Hq by using the exact partition function of the one-dimensional model. The Fisher zeros of the Potts model in an external magnetic eld are discussed for any real value of Q  0. The Potts zeros in the complex Q plane for nonzero magnetic eld are studied for the ferromagnetic and the antiferromagnetic Potts models. All Fisher zeros lie on a circle in the complex y = eJ plane for Q > 1 and Hq  0, except Q = 2 (Ising model) whose zeros lie on the imaginary axis. Some Fisher zeros lie on the positive real axis, but they are not physical. All Potts zeros of the ferromagnetic model lie on a circle for Hq  0. All Potts zeros of the antiferromagnetic model with Hq < 0 also lie on a circle for (x + 1)1, where a = yand x = e Hq . The densities of zeros are also calculated and discussed. The density of zeros at the Fisher edge singularity diverges, and the edge critical exponents at the singularity satisfy a scaling law. A Potts edge singularity exists in the complex Q plane and is similar to the Fisher edge singularity in the complex temperature plane.


The properties of the partition function zeros in the complex temperature plane (Fisher zeros) and in the complex Q plane (Potts zeros) are investigated for the Q-state Potts model in an arbitrary nonzero external magnetic eld Hq by using the exact partition function of the one-dimensional model. The Fisher zeros of the Potts model in an external magnetic eld are discussed for any real value of Q  0. The Potts zeros in the complex Q plane for nonzero magnetic eld are studied for the ferromagnetic and the antiferromagnetic Potts models. All Fisher zeros lie on a circle in the complex y = eJ plane for Q > 1 and Hq  0, except Q = 2 (Ising model) whose zeros lie on the imaginary axis. Some Fisher zeros lie on the positive real axis, but they are not physical. All Potts zeros of the ferromagnetic model lie on a circle for Hq  0. All Potts zeros of the antiferromagnetic model with Hq < 0 also lie on a circle for (x + 1)1, where a = yand x = e Hq . The densities of zeros are also calculated and discussed. The density of zeros at the Fisher edge singularity diverges, and the edge critical exponents at the singularity satisfy a scaling law. A Potts edge singularity exists in the complex Q plane and is similar to the Fisher edge singularity in the complex temperature plane.