Potts models on hierarchical lattices and Renormalization Group dynamics

Jacopo De Simoi; Stefano Marmi

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arXiv · 0708.0616

Potts models on hierarchical lattices and Renormalization Group dynamics

Jacopo De Simoi·Stefano Marmi

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Abstract

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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Jacopo De Simoi, Stefano Marmi. 2008-08-03. Potts models on hierarchical lattices and Renormalization Group dynamics. https://arxiv.org/abs/0708.0616

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