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

A. Comtet·S. Nechaev·R. Voituriez
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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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A. Comtet, S. Nechaev, R. Voituriez. 2000-04-28. Multifractality in uniform hyperbolic lattices and in quasi-classical Liouville field theory. https://arxiv.org/abs/cond-mat/0004491

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