Scaling of Particle Trajectories on a Lattice II: The Critical Region
| dc.creator | Cao, Meng-she | |
| dc.creator | Cohen, E. G. D. | |
| dc.date | 1996-08-29 | |
| dc.date.accessioned | 2026-07-07T03:08:50Z | |
| dc.date.available | 2026-07-07T03:08:50Z | |
| dc.description | 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 $n_S$ and $h(x)$ related to the trajectory size $R_S$ (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 $σ=0.43\approx 3/7$ as was found at criticality. In contrast to previous assumptions of an exponential dependence of $n_S$ on $S$, the Gaussian functions lead to a stretched exponential dependence of $n_S$ on $S$, $n_S\sim e^{-S^{6/7}}$. However, for the rotator model on the partially occupied square lattice, an alternative scaling function near criticality is found, leading to a new exponent $σ'=1.6\pm0.3$ and a super exponential dependence of $n_S$ 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. | |
| dc.description | 22 pages LaTex and 18 postscript figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9608160 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9608160 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/27656 | |
| dc.subject | Condensed Matter | |
| dc.title | Scaling of Particle Trajectories on a Lattice II: The Critical Region | |
| dc.type | text |