2002/07/31 by L. N. Shchur, Lev Shchur, Lev N. Shchur +2 · 1 citation
Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Condensed matter physics #Critical dimension #Critical exponent #Criticality #Crossover #Electrical resistivity and conductivity #Exponent #Mathematical analysis #Mathematics #Multiplicity (mathematics) #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #Phase transition #Physics #Quantum mechanics #Random Matrices and Applications #Self-organized criticality #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #hep-lat #math-ph #math.MP
paper · pdf · doi:10.1134/1.1528706
published as JETP Lett. 76 (2002) 475-480; Pisma Zh.Eksp.Teor.Fiz. 76 (2002) 553-558 · 5 pages, 4 figures, 4 tables
openalex publication_date 2002/10/01 · arxiv created 2002/10/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The probabilities of clusters spanning a hypercube of dimension two to seven along one axis of a percolation system under criticality were investigated numerically. We used a modified Hoshen-Kopelman algorithm combined with Grassberger’s “go with the winner” strategy for the site percolation. We carried out a finite-size analysis of the data and found that the probabilities confirm Aizenman’s proposal of the multiplicity exponent for dimensions three to five. A crossover to the mean-field behavior around the upper critical dimension is also discussed.