Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2012-01-14
Physics
Condensed Matter
Statistical Mechanics
33 pages, 23 figures
Scientific paper
We present a Monte Carlo study of the bond and the site directed percolation model on the $(d+1)$-dimensional simple-cubic and the body-centered-cubic lattices with $d=2$ to 7, as well as on the square, triangular, honeycomb, and kagom\'e lattices for $d=1$. With a cumulative-probability and a linking-hashing technique, the simulation is reasonably efficient, independent of $d$, and can be up to very large virtual lattices (e.g., more than $10^{27}$ sites for $d=7$). A dimensionless ratio $Q_\bcN$ is defined to locate the percolation threshold $p_c$. Universal scaling of $Q_\bcN$ near $p_c$ is checked, and accordingly the $Q_\bcN$ data for systems in the same dimension are simultaneously analyzed by a formula, in which universal parameters occur only once. In comparison with existing results, our estimates for $p_c$ are comparable or somewhat better for $d=1$, and much more precise for $d>1$. Extensive simulations are then carried out at the estimated thresholds. The probability distribution and the finite-size scaling of several quantities are studied. The critical exponents are accurately determined. At the upper critical dimensionality $d_c=4$, logarithmic corrections are clearly observed and found to be well described by the theoretical predictions. For $d>d_c$, the mean-field behavior is confirmed.
Deng Youjin
Liu Qingquan
Wang Junfeng
No associations
LandOfFree
A high-precision Monte Carlo study of directed percolation in (1+1) and higher dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A high-precision Monte Carlo study of directed percolation in (1+1) and higher dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A high-precision Monte Carlo study of directed percolation in (1+1) and higher dimensions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-693889