Two-dimensional percolation model with long-range interaction
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916961157382144 |
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| author | Liu, Ziyu Xiao, Tianning Fan, Zhijie Deng, Youjin |
| author_facet | Liu, Ziyu Xiao, Tianning Fan, Zhijie Deng, Youjin |
| contents | We perform large-scale simulations of the two-dimensional long-range bond percolation model with algebraically decaying percolation probabilities $\sim 1/r^{2+σ}$, using both conventional ensemble and event-based ensemble methods for system sizes up to $L=16384$. We accurately determine the critical points, the universal values of several dimensionless quantities, and the corresponding critical exponents. Our results provide compelling evidence that the system undergoes a crossover from short-range to long-range universality at $σ= 2$, in contradiction to Sak's criterion. Notably, we observe a pronounced jump in the universal values and critical exponents at $σ= 2$, a feature absent from previous studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-dimensional percolation model with long-range interaction Liu, Ziyu Xiao, Tianning Fan, Zhijie Deng, Youjin Statistical Mechanics We perform large-scale simulations of the two-dimensional long-range bond percolation model with algebraically decaying percolation probabilities $\sim 1/r^{2+σ}$, using both conventional ensemble and event-based ensemble methods for system sizes up to $L=16384$. We accurately determine the critical points, the universal values of several dimensionless quantities, and the corresponding critical exponents. Our results provide compelling evidence that the system undergoes a crossover from short-range to long-range universality at $σ= 2$, in contradiction to Sak's criterion. Notably, we observe a pronounced jump in the universal values and critical exponents at $σ= 2$, a feature absent from previous studies. |
| title | Two-dimensional percolation model with long-range interaction |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2509.18035 |