Abstract
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 <Δ>=0 (Δ is the perturbation potential resulting from moving the bonds); second, the condition <Δ>=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.
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Communicated by J. L. Lebowitz
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Yang, Z.R., Song, L. Application of bond-moving renormalization-group approach to fractal lattices. J Stat Phys 88, 1409–1418 (1997). https://doi.org/10.1007/BF02732443
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DOI: https://doi.org/10.1007/BF02732443