Dimension of the loop-erased random walk in three dimensions
Abstract
We measure the fractal dimension of loop-erased random walk (LERW) in three dimensions and estimate that it is 1.62400±0.00005 . 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.
- Publication:
-
Physical Review E
- Pub Date:
- December 2010
- DOI:
- 10.1103/PhysRevE.82.062102
- arXiv:
- arXiv:1008.1147
- Bibcode:
- 2010PhRvE..82f2102W
- Keywords:
-
- 05.40.Fb;
- 64.60.De;
- 45.70.Cc;
- Random walks and Levy flights;
- Statistical mechanics of model systems;
- Static sandpiles;
- granular compaction;
- Condensed Matter - Statistical Mechanics;
- 60C05;
- 82B20;
- 05C05
- E-Print:
- 4 pages, 4 figures. v2 has more data, minor additional changes