Scaling of loop-erased walks in 2 to 4 dimensions
Abstract
We simulate loop-erased random walks on simple (hyper-)cubic lattices of dimensions 2,3, and 4. These simulations were mainly motivated to test recent two loop renormalization group predictions for logarithmic corrections in , simulations in lower dimensions were done for completeness and in order to test the algorithm. In , we verify with high precision the prediction , where the number of steps after erasure scales with the number of steps before erasure as . In we again find a power law, but with an exponent different from the one found in the most precise previous simulations: . Finally, we see clear deviations from the naive scaling in . While they agree only qualitatively with the leading logarithmic corrections predicted by several authors, their agreement with the two-loop prediction is nearly perfect.
Keywords
Cite
@article{arxiv.0905.3440,
title = {Scaling of loop-erased walks in 2 to 4 dimensions},
author = {Peter Grassberger},
journal= {arXiv preprint arXiv:0905.3440},
year = {2015}
}
Comments
3 pages, including 3 figures