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| Hauptseite > Publikationsdatenbank > Scaling of Loop-Erased Walks in 2 to 4 Dimensions |
| Hauptseite > Publikationsdatenbank > Scaling of Loop-Erased Walks in 2 to 4 Dimensions |
| Journal Article | PreJuSER-9984 |
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)
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