• Corpus ID: 220935791

# Random-length Random Walks and Finite-size Scaling on high-dimensional hypercubic lattices I: Periodic Boundary Conditions

```@article{Zhou2020RandomlengthRW,
title={Random-length Random Walks and Finite-size Scaling on high-dimensional hypercubic lattices I: Periodic Boundary Conditions},
author={Zongzheng Zhou and Jens Grimm and Youjin Deng and Timothy M. Garoni},
journal={arXiv: Mathematical Physics},
year={2020}
}```
• Published 3 August 2020
• Mathematics
• arXiv: Mathematical Physics
We study a general model of random-length random walks on discrete tori, and show that the mean walk length controls the scaling of the two-point function. We conjecture that on tori of dimension at least 5, the two-point functions of the Ising model and self-avoiding walk display the same scaling as the random-length random walk, not only at criticality, but also for a broad class of scaling windows/pseudocritical points. This conjecture is supported by extensive Monte Carlo simulations of the…
9 Citations

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