1996/08/29 by Meng-she Cao, Cao, Meng-she, E. G. D. Cohen +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9608160
22 pages LaTex and 18 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 in the critical region are investigated. We study numerically two scaling functions: f(x) related to the trajectory length distribution nS and h(x) related to the trajectory size RS (gyration radius) as introduced by Stauffer for the percolation problem, where S is the length of a closed trajectory. The scaling function f(x) is in most cases found to be symmetric double Gaussians with the same characteristic size exponent σ=0.43≈ 3/7 as was found at criticality. In contrast to previous assumptions of an exponential dependence of nS on S, the Gaussian functions lead to a stretched exponential dependence of nS on S, nS∼ e^-S6/7. However, for the rotator model on the partially occupied square lattice, an alternative scaling function near criticality is found, leading to a new exponent σ'=1.6±0.3 and a super exponential dependence of nS on S. The appearance of the same exponent σ=3/7 describing the behavior at and near the critical point is discussed. Our numerical simulations show that h(x) is essentially a constant, which depends on the type of lattice and on the concentration of the scatterers.