Loop-erased random walk as a spin system observable

Abstract

The determination of the Hausdorff dimension of the scaling limit of loop-erased random walk is closely related to the study of the one-point function of loop-erased random walk, i.e., the probability a loop-erased random walk passes through a given vertex. Recent work in the theoretical physics literature has investigated the Hausdorff dimension of loop-erased random walk in three dimensions by applying field theory techniques to study spin systems that heuristically encode the one-point function of loop-erased random walk. Inspired by this, we introduce two different spin systems whose correlation functions can be rigorously shown to encode the one-point function of loop-erased random walk.

arXiv commentAccepted version

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Cited by in corpus (4)

• Renormalization group for measurement and entanglement phase transitions
• An exact mapping between loop-erased random walks and an interacting field theory with two fermions and one boson
• Roughness and critical force for depinning at 3-loop order
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories