Scaling of Loop-Erased Walks in 2 to 4 Dimensions View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2009-07

AUTHORS

Peter Grassberger

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 d=4, simulations in lower dimensions were done for completeness and in order to test the algorithm. In d=2, we verify with high precision the prediction D=5/4, where the number of steps n after erasure scales with the number N of steps before erasure as n∼ND/2. In d=3 we again find a power law, but with an exponent different from the one found in the most precise previous simulations: D=1.6236±0.0004. Finally, we see clear deviations from the naive scaling n∼N in d=4. While they agree only qualitatively with the leading logarithmic corrections predicted by several authors, their agreement with the two-loop prediction is nearly perfect. More... »

PAGES

399-404

References to SciGraph publications

Journal

TITLE

Journal of Statistical Physics

ISSUE

2

VOLUME

136

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10955-009-9787-0

DOI

http://dx.doi.org/10.1007/s10955-009-9787-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1044932025


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