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.
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Fedorenko, A.A., Le Doussal, P. & Wiese, K.J. Field Theory Conjecture for Loop-Erased Random Walks. J Stat Phys 133, 805–812 (2008). https://doi.org/10.1007/s10955-008-9642-8
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DOI: https://doi.org/10.1007/s10955-008-9642-8