Application of bond-moving renormalization-group approach to fractal lattices

We investigate the application of the Migdal-Kadanoff bond-moving renormalization group (RG) approach to fractal lattices. We find the following two results: first, for inhomogeneous interaction lattice models, bond moving involving inequivalent bonds is unsuitable because it violates the condition [Delta] = 0 (Delta is the perturbation potential resulting from moving the bonds); second, the condition [Delta] = 0 does not uniquely determine the way to move bonds; different choices of bond moving yield different RG recursion relations and corresponding fixed points, which makes the conclusions concerning the phase transition quite uncertain.