Field theory conjecture for loop-erased random walks

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 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

References in corpus (14)

• Renormalization of pinned elastic systems: how does it work beyond one loop ?
• 2-loop Functional Renormalization Group Theory of the Depinning Transition
• Scaling of waves in the Bak-Tang-Wiesenfeld sandpile model
• Avalanches and the Renormalization Group for Pinned Charge-Density Waves
• Statistics of static avalanches in a random pinning landscape
• Measuring functional renormalization group fixed-point functions for pinned manifolds
• Scaling in self-organized criticality from interface depinning?
• Self Avoiding Walks in Four Dimensions: Logarithmic Corrections
• Higher correlations, universal distributions and finite size scaling in the field theory of depinning
• Universal distribution of threshold forces at the depinning transition
• Distribution of sizes of erased loops of loop-erased random walks in two and three dimensions
• Depinning transition at the upper critical dimension
• Disordered periodic systems at the upper critical dimension
• Exponents and bounds for uniform spanning trees in d dimensions

Cited by in corpus (11)

• Size distributions of shocks and static avalanches from the Functional Renormalization Group
• Fractal dimensions of self-avoiding walks and Ising high-temperature graphs in 3D conformal bootstrap
• An exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media
• Field Theories for Loop-Erased Random Walks
• The dimension of loop-erased random walk in 3D
• Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric ${\varphi }^4$ theory with $n\to -2$ and loop-erased random walks
• Some Properties of Sandpile Models as Prototype of Self-Organized Critical Systems
• Scaling of loop-erased walks in 2 to 4 dimensions
• An exact mapping between loop-erased random walks and an interacting field theory with two fermions and one boson
• Loop-erased random walk as a spin system observable
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles