Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-01-11
J. Phys. A 33 (2000) 5631-5652
Physics
Condensed Matter
Statistical Mechanics
28 pages, 11 eps-figures (enclosed)
Scientific paper
10.1088/0305-4470/33/32/302
Multifractal properties of the distribution of topological invariants for a model of trajectories randomly entangled with a nonsymmetric lattice of obstacles are investigated. Using the equivalence of the model to random walks on a locally nonsymmetric tree, statistical properties of topological invariants, such as drift and return probabilities, have been studied by means of a renormalization group (RG) technique. The comparison of the analytical RG--results with numerical simulations as well as with the rigorous results of P.Gerl and W.Woess demonstrates clearly the validity of our approach. It is shown explicitly by direct counting for the discrete version of the model and by conformal methods for the continuous version that multifractality occurs when local uniformity of the phase space (which has an exponentially large number of states) has been broken.
Nechaev Sergei
Voituriez Raphael
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