Loop-Erased Random Walk as a Spin System Observable

Helmuth, Tyler; Shapira, Assaf

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.

Citation

Helmuth, T., & Shapira, A. (2020). Loop-Erased Random Walk as a Spin System Observable. Journal of Statistical Physics, 181(4), 1306-1322. https://doi.org/10.1007/s10955-020-02628-7

• Journal Article Type: Article
• Acceptance Date: Aug 17, 2020
• Online Publication Date: Aug 24, 2020
• Publication Date: 2020-11
• Deposit Date: Aug 25, 2020
• Publicly Available Date: Aug 24, 2021
• Journal: Journal of Statistical Physics
• Print ISSN: 0022-4715
• Electronic ISSN: 1572-9613
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 181
• Issue: 4
• Pages: 1306-1322
• DOI: https://doi.org/10.1007/s10955-020-02628-7
• Public URL: https://durham-repository.worktribe.com/output/1263140
• Related Public URLs: https://arxiv.org/abs/2003.10928