The Yang-Lee edge singularity for the Ising model on two Sierpinski fractal lattices

We study the distribution of zeros of the partition function of the ferromagnetic Ising model near the Yang-Lee edge on two Sierpiski-type lattices. We have shown that relevant correlation length displays a logarithmic divergence near the edge, ξYL∼|ln(∂h)|Φ where Φ is a constant and δh distance from the edge, in the case of a modified Sierpinski gasket with a nonuniform coordination number. It is demonstrated that this critical behavior can be related to the critical behavior of a simple zero-field Gaussian model of the same structure. We have shown that there is no such connection between these two models on a second lattice that has a uniform coordination number. These findings suggest that fluctuations of the lattice coordination number of a nonhomogeneous self-similar structure exert the crucial influence on the critical behavior of both models.