Considering the sets of the points corresponding to the phase transitions of the Potts model on the diamond hierarchical lattice for antiferromagnetic coupling, it is shown that these sets are the Julia sets of a family of rational mappings. In this paper, we prove that they may be buried points of J(T_λ(z)) for some λ ∈ R. Further, the asymptotic formula of the Hausdorff dimension of the Julia set is given as λ →∞, which gives a lower bound the Hausdorff dimension of the Julia set of J(T_λ(z)). Finally, other topo...
