Field theory conjecture for loop-erased random walks
Andrei A. Fedorenko, Pierre Le Doussal, Kay Jörg Wiese
CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France
Abstract
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
ε = 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.
arXiv:0803.2357 [pdf]
J. Stat. Phys. 133, 805-812 (2008) [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.