Sandpiles with finite-range interactions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915497795125248 |
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| author | Shoja-Daliklidash, Abbas Najafi, Morteza Nattagh |
| author_facet | Shoja-Daliklidash, Abbas Najafi, Morteza Nattagh |
| contents | We investigate the sandpile model with Yukawa-type interactions, whose effective range is tuned by an external parameter $R$. Our results reveal that at specific values of $R$, the system exhibits giant avalanches that span the system, leading to percolation. The probability of such giant avalanches demonstrates two distinct regimes as a function of $R$: for sufficiently small $R$, it increases monotonically, whereas for large $R$ it undergoes threshold dynamics, so that at certain values of $R$, the percolation probability exhibits abrupt jumps. We refer it to as \textit{pseudo-percolation transitions}, based on which we propose a hierarchical percolation model at the mean-field level: each percolation transition corresponds to percolation within a disc of radius $R$. We further examine both local and global geometrical observables. The local quantities include avalanche size, mass, and duration and sub-avalanche mass, while for the global characterization we analyze the loop length and gyration radius of the external perimeter, as well as the mass of sub-avalanches. Remarkably, all these observables exhibit power-law scaling for all values of $R$, with exponents that vary systematically with $R$. Notably, in the vicinity of the pseudo-percolation transition points, the exponents approach characteristic values, signaling a distinct critical behavior. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_13500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sandpiles with finite-range interactions Shoja-Daliklidash, Abbas Najafi, Morteza Nattagh Statistical Mechanics We investigate the sandpile model with Yukawa-type interactions, whose effective range is tuned by an external parameter $R$. Our results reveal that at specific values of $R$, the system exhibits giant avalanches that span the system, leading to percolation. The probability of such giant avalanches demonstrates two distinct regimes as a function of $R$: for sufficiently small $R$, it increases monotonically, whereas for large $R$ it undergoes threshold dynamics, so that at certain values of $R$, the percolation probability exhibits abrupt jumps. We refer it to as \textit{pseudo-percolation transitions}, based on which we propose a hierarchical percolation model at the mean-field level: each percolation transition corresponds to percolation within a disc of radius $R$. We further examine both local and global geometrical observables. The local quantities include avalanche size, mass, and duration and sub-avalanche mass, while for the global characterization we analyze the loop length and gyration radius of the external perimeter, as well as the mass of sub-avalanches. Remarkably, all these observables exhibit power-law scaling for all values of $R$, with exponents that vary systematically with $R$. Notably, in the vicinity of the pseudo-percolation transition points, the exponents approach characteristic values, signaling a distinct critical behavior. |
| title | Sandpiles with finite-range interactions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2509.13500 |