We introduce a class of deterministic ultrametric fractal models in d=2, which are expected to mimic some dynamic properties of random walks. The relative diffusion and dc conduction problems are solved exactly, showing both universal and nonuniversal regimes, as already found in simpler d=1 hierarchical structures. For a natural choice of parameters, the model’s spectral dimension takes the Alexander-Orbach value (4/3, which was also conjectured for random walks in d=2. The problem of self-avoiding walks on these structures is also briefly discussed.

• Received 27 June 1989

DOI:https://doi.org/10.1103/PhysRevA.40.5299