Field theory conjecture for loop-erased random walks

Fedorenko, Andrei A.; Doussal, Pierre Le; Wiese, Kay Joerg

Field theory conjecture for loop-erased random walks

Authors

Fedorenko, Andrei A.

Doussal, Pierre Le

Wiese, Kay Joerg

Description

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.
5 pages