High-precision Monte Carlo study of directed percolation in (d+1) dimensions.
We present a Monte Carlo study of the bond- and site-directed (oriented) percolation models in (d+1) dimensions on simple-cubic and body-centered-cubic lattices, with 2 ≤ d ≤ 7. A dimensionless ratio is defined, and an analysis of its finite-size scaling produces improved estimates of percolation thresholds. We also report improved estimates for the standard critical exponents. In addition, we study the probability distributions of the number of wet sites and radius of gyration, for 1 ≤ d ≤ 7.
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and School of Electronic Science and Applied Physics, Hefei University of Technology, Hefei 230009, China.
Junfeng
J
Wang
Zongzheng
Z
Zhou
Qingquan
Q
Liu
Timothy M
TM
Garoni
Youjin
Y
Deng