On the Yang–Lee edge singularity for Ising model on nonhomogeneous structures

We studied distribution of zeros of the partition function of ferromagnetic Ising model near the Yang–Lee edge on two self-similar structures. We have shown that the nature of associated critical behavior crucially depends on the local lattice structure: If the sites of higher coordination number make an infinite connected cluster then we find an usual power-law behavior, while a logarithmic divergence of the correlation length develops near the edge in the case that these sites make only finite islands. We reveal also a close connection between Yang–Lee edge critical behavior and critical behavior of a simple zero-field Gaussian model on the same structures.