2008/07/23 by Viktoria Blavatska, Wolfhard Janke · 28 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Cluster (spacecraft) #Complex Systems and Time Series Analysis #Computer science #Critical exponent #Distribution (mathematics) #Fractal #Geometry #Gravitational singularity #Mathematical analysis #Mathematics #Multifractal system #Percolation (cognitive psychology) #Percolation critical exponents #Physics #Quantum mechanics #Scaling #Scaling law #Space (punctuation) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.soft
paper · pdf · doi:10.1103/physrevlett.101.125701
published in Physical Review Letters 101(12), 125701 (American Physical Society) · 4 pages
arxiv created 2008/07/23 · openalex publication_date 2008/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider self-avoiding walks on the backbone of percolation clusters in space dimensions d=2,3,4. Applying numerical simulations, we show that the whole multifractal spectrum of singularities emerges in exploring the peculiarities of the model. We obtain estimates for the set of critical exponents that govern scaling laws of higher moments of the distribution of percolation cluster sites visited by self-avoiding walks, in a good correspondence with an appropriately summed field-theoretical epsilon=6-d expansion [H.-K. Janssen and O. Stenull, Phys. Rev. E 75, 020801(R) (2007)10.1103/PhysRevE.75.020801].