Potts models on hierarchical lattices and Renormalization Group dynamics

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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

Keywords

Statistical Mechanics, Dynamical Systems

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/166186

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.0616
 http://arxiv.org/abs/0708.0616

Collections

arXiv