Zeros of the partition function of Ising models on fractal lattices

Exact results are presented for the density of zeros of the partition function for Ising models on fractal lattices. For nearest-neighbor ferromagnetic interactions and real temperatures T, the zeros lie on the unit circle in the complex activity plane but leave the circle at high temperatures when four-spin interactions are included. The density of zeros exhibits a scaling form near the Yang-Lee edge and nontrivial values of the edge exponent σ are found which are independent of T for all T>0 and independent of the spin magnitude. Some results for the position of the zeros in the complex T plane are also given.