Random-Length Random Walks and Finite-Size Scaling in High Dimensions

Zongzheng Zhou, Jens Christian Grimm, Sheng Fang, Youjin Deng, Tim Garoni

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2 Citations (Scopus)


We address a long-standing debate regarding the finite-size scaling (FSS) of the Ising model in high dimensions, by introducing a random-length random walk model, which we then study rigorously. We prove that this model exhibits the same universal FSS behavior previously conjectured for the self-avoiding walk and Ising model on finite boxes in high-dimensional lattices. Our results show that the mean walk length of the random walk model controls the scaling behavior of the corresponding Green's function. We numerically demonstrate the universality of our rigorous findings by extensive Monte Carlo simulations of the Ising model and self-avoiding walk on five-dimensional hypercubic lattices with free and periodic boundaries.

Original languageEnglish
Article number185701
Number of pages5
JournalPhysical Review Letters
Issue number18
Publication statusPublished - 2 Nov 2018

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