Phys. Rev. E 82, 062102 (2010) [4 pages]Dimension of the loop-erased random walk in three dimensionsReceived 10 August 2010; published 16 December 2010 We measure the fractal dimension of loop-erased random walk (LERW) in three dimensions and estimate that it is 1.624 00±0.000 05. LERW is closely related to the uniform spanning tree and the Abelian sandpile model. We simulated LERW on both the cubic and face-centered-cubic lattices; the corrections to scaling are slightly smaller for the face-centered-cubic lattice. ©2010 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.82.062102
DOI:
10.1103/PhysRevE.82.062102
PACS:
05.40.Fb, 64.60.De, 45.70.Cc
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