1996/08/29 by Meng-she Cao, Cao, Meng-she, E. G. D. Cohen +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Diffusion and Search Dynamics #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9608159
33 pages LaTex and 27 postscript figures
arxiv created 1996/08/29 · arxiv updated 2009/11/30
The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. For most concentrations of the scatterers the trajectories close exponentially fast. For special critical concentrations infinitely extended trajectories can occur which exhibit a scaling behavior similar to that of the perimeters of percolation clusters. In addition to the two critical exponents τ=15/7 and df=7/4 found before, the critical exponent σ=3/7, which is associated with the scaling function for trajectory size away from criticality, also appears. This exponent determines structural scaling properties of closed trajectories of finite size when they approach infinity, at criticality. New scaling behavior was found for the square lattice partially occupied by rotators, indicating a different universality class from that of percolation clusters. An argument for the scaling behavior found along the critical lines is presented.