• 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}
}
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… 
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