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

2000/04/28 by A. Comtet, S. Nechaev, R. Voituriez · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #math-ph #math.MP

paper · pdf

published as J. Stat. Phys. 102, 1/2 (2001) · 24 pages, 8 eps-figures

arxiv created 2000/04/28 · arxiv updated 2009/11/30

Abstract

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.

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