Problem of Universality in Phase Transitions on Hierarchical Lattices

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Abstract
Fundamental problems associated with universality in phase transitions on hierarchical lattices are examined. It is shown that the critical properties actually depend on more details of the lattice than are usually acknowledged. The claim that the fractal dimension and the connectivity serve as criteria for universality is called into question. There is a lack of conclusive evidence, theoretical or experimental, to establish the validity of universality on hierarchical lattices. It therefore seems that universality is but an extrapolated hypothesis that can hope to hold only in a very restricted or approximate sense. It is more likely that the principle of universality is violated.