Field theory conjecture for loop-erased random walks

Details Field theory conjecture for loop-erased random walks Field theory conjecture for loop-erased random walks

2008-03-16

arxiv.org/abs/0803.2357v2

J. Stat. Phys. 133, 805-812 (2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages

Scientific paper

10.1007/s10955-008-9642-8

We give evidence that the functional renormalization group (FRG), developed to study disordered systems, may provide a field theoretic description for the loop-erased random walk (LERW), allowing to compute its fractal dimension in a systematic expansion in epsilon=4-d. Up to two loop, the FRG agrees with rigorous bounds, correctly reproduces the leading logarithmic corrections at the upper critical dimension d=4, and compares well with numerical studies. We obtain the universal subleading logarithmic correction in d=4, which can be used as a further test of the conjecture.

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