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

Abstract

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, ξ yl ∼ | ln(δ 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 selfsimilar structure exert the crucial influence on the critical behavior of both models. © 2010 IOP Publishing Ltd.