Critical exponents, Julia sets and lattice structures

We study the Ising model defined on a class of hierarchical lattices in ord er to analyze the geometric effects on the critical exponents and on the gl obal scaling properties of the Julia sets consisting of the Yang-Lee zeros of the partition functions. Using the exact renormalization map of the mode l with an external field we study how the critical behaviors, including the location of the critical temperature and the critical exponents, vary with the geometric structure. The generalized dimensions D-q and the sigularity spectra f(alpha) of the Julia sets of the renormalization maps for differe nt hierarchies are calculated, and variations caused by their geometric str ucture are also discussed.