Re-examination of Yang-Lee zeros of the anisotropic Ising models on square, triangular and honeycomb lattices

We have determined the zeros of the partition functions of the anisotropic Ising models on square, triangular and honeycomb lattices in the absence of a magnetic field, with arbitrary combinations of interactions. It is found that the zeros are generally distributed over areas. However, the zeros near the positive real axis are distributed on the unit circle in a complex plane, with the zero density g (θ)~|θ|, which leads to logarithmic singularity of the free energy. Our results generalize Fisher's results for isotropic cases.