Yang-Lee edge singularity on fractals

Exact results are presented for the density of zeros of the partition function for Ising models on fractal lattices. For nearest-neighbor ferromagnetic interactions, 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 edge, and the value of the edge exponent $\sigma$ is found to be independent of $T$ for all $T>\mathrm{}0\mathrm{}$.