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Author

Zi-Yu Liu

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Preprint Sep 2026

Long-range self-avoiding walk in one dimension: a Monte Carlo study

We study the one-dimensional long-range self-avoiding walk in the grand-canonical ensemble where the statistical weight of a jump of length $r$ decays algebraically as $r^{-(d+\sigma)}$. Using large-scale Monte Carlo simulations with an efficient irreversible update scheme, we obtain high-precision estimates of the cri...

Jiang Zhou, Zi-Yu Liu, Peng-Cheng Hou et al. · 0 citations
Preprint Aug 2026

Two-dimensional percolation with algebraically decaying interactions II: Critical exponents in the long-range regime

We present a comprehensive Monte Carlo study of two-dimensional bond percolation with algebraically decaying connection probabilities $p(r)\propto 1/r^{2+\sigma}$, establishing the universality diagram in the long-range (LR) regime for $\sigma\le2$. Using the event-based ensemble method, we simulate systems with linear...

Zi-Yu Liu, Tianning Xiao, Zhi-Jie Fan et al. · 2 citations

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