Multifractality in uniform hyperbolic lattices and in quasi-classical Liouville field theory

Alain Comtet 1, Sergei K. Nechaev 1, Raphael Voituriez 1

Journal of Statistical Physics 102 (2001) 203-230

We introduce a deterministic model defined on a two dimensional hyperbolic lattice. This model provides an example of a non random system whose multifractal behaviour has a number theoretic origin. We determine the multifractal exponents, discuss the termination of multifractality and conjecture the geometric origin of the multifractal behavior in Liouville quasi--classical field theory.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud