Density of zeros of the ferromagnetic Ising model on a family of fractals

Abstract

We studied distribution of zeros of the partition function of the ferromagnetic Ising model near the Yang-Lee edge on a family of Sierpinski gasket lattices whose members are labeled by an integer b (2≤b<∞). The obtained exact results on the first seven members of this family show that, for b≥4, associated correlation length diverges more slowly than any power law when distance δh from the edge tends to zero, ξ YL∼ exp[ln(b)√|ln(δh)|/ln(λ 0)], λ 0 being a decreasing function of b. We suggest a possible scenario for the emergence of the usual power-law behavior in the limit of very large b when fractal lattices become almost compact. © 2012 American Physical Society.