Journal Article

PreJuSER-9984

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Scaling of Loop-Erased Walks in 2 to 4 Dimensions

Grassberger, P.FZJ*

2009
Springer Science + Business Media B.V. New York, NY [u.a.]

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Please use a persistent id in citations: doi:10.1007/s10955-009-9787-0

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 similar to N (D/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 similar to 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.

Keyword(s): J ; Loop-erased walks (auto) ; Critical exponents (auto) ; Logarithmic corrections (auto)

Note: Record converted from VDB: 12.11.2012

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Contributing Institute(s):

1. Jülich Supercomputing Centre (JSC)

Research Program(s):

1. Scientific Computing (P41)

Appears in the scientific report 2009
Notes: Nachtrag

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