paper

Logarithmic corrections in (4+1)-dimensional directed percolation

arXiv:0904.0804 · doi:10.1103/PhysRevE.79.052104

Abstract

We simulate directed site percolation on two lattices with 4 spatial and 1 time-like dimensions (simple and body-centered hypercubic in space) with the standard single cluster spreading scheme. For efficiency, the code uses the same ingredients (hashing, histogram re-weighing, and improved estimators) as described in Phys. Rev. {\bf E 67}, 036101 (2003). Apart from providing the most precise estimates for on these lattices, we provide a detailed comparison with the logarithmic corrections calculated by Janssen and Stenull [Phys. Rev. {\bf E 69}, 016125 (2004)]. Fits with the leading logarithmic terms alone would give estimates of the powers of these logarithms which are too big by typically 50%. When the next-to-leading terms are included, each of the measured quantities (the average number of sites wetted at time , their average distance from the seed, and the probability of cluster survival) can be fitted nearly perfectly. But these fits would not be mutually consistent. With a consistent set of fit parameters, one obtains still much improvement over the leading log - approximation. In particular we show that there is one combination of these three observables which seems completely free of logarithmic terms.

several minor changes; to be published in Phys. Rev. E

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