Potts models on hierarchical lattices and Renormalization Group dynamics

Details Potts models on hierarchical lattices and Renormalization Group dynamics Potts models on hierarchical lattices and Renormalization Group dynamics

2007-08-04

arxiv.org/abs/0708.0616v3

Physics

Condensed Matter

Statistical Mechanics

21 pages, 7 figures; v3 revised, some issues corrected

Scientific paper

We prove that the generator of the renormalization group of Potts models on hierarchical lattices can be represented by a rational map acting on a finite-dimensional product of complex projective spaces. In this framework we can also consider models with an applied external magnetic field and multiple-spin interactions. We use recent results regarding iteration of rational maps in several complex variables to show that, for some class of hierarchical lattices, Lee-Yang and Fisher zeros belong to the unstable set of the renormalization map.

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