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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.12309 |
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| _version_ | 1866909994112253952 |
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| author | Levi, Raz Halifa Kantor, Yacov |
| author_facet | Levi, Raz Halifa Kantor, Yacov |
| contents | We consider a correlated site percolation problem on a cubic lattice of size $L^3$, with $16\le L\le 512$. The sites of an initially full lattice are removed by a random walk of ${\cal N}=uL^3$ steps. When the parameter $u$ crosses a threshold $u_c=3.15$, a large system transitions between percolating and non-percolating states. We study the $L$-dependence of the mean mass (number of sites) $M_r$ of the $r$th largest cluster, as well as $r$-dependence of $M_r$ for various system sizes $L$ at $u_c$. We demonstrate that $M_r\sim L^{5/2}/r^{5/6}$ for moderate or large $L$ and $r\gg 1$, and also conclude that for {\em any} $r$ the fractal dimensions of the clusters are $5/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12309 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large clusters in a correlated percolation model Levi, Raz Halifa Kantor, Yacov Statistical Mechanics We consider a correlated site percolation problem on a cubic lattice of size $L^3$, with $16\le L\le 512$. The sites of an initially full lattice are removed by a random walk of ${\cal N}=uL^3$ steps. When the parameter $u$ crosses a threshold $u_c=3.15$, a large system transitions between percolating and non-percolating states. We study the $L$-dependence of the mean mass (number of sites) $M_r$ of the $r$th largest cluster, as well as $r$-dependence of $M_r$ for various system sizes $L$ at $u_c$. We demonstrate that $M_r\sim L^{5/2}/r^{5/6}$ for moderate or large $L$ and $r\gg 1$, and also conclude that for {\em any} $r$ the fractal dimensions of the clusters are $5/2$. |
| title | Large clusters in a correlated percolation model |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2601.12309 |