High-precision Monte Carlo study of directed percolation in (d+1) dimensions

Junfeng Wang, Zongzheng Zhou, Qingquan Liu, Timothy M. Garoni, Youjin Deng

Published 2012-01-14, updated 2013-10-10Version 3

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 $2 \leq d \leq 7$. 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 $1 \leq d \leq 7$.