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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2403.02789 |
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| _version_ | 1866917724171534336 |
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| author | Yang, Liwenying Li, Ming |
| author_facet | Yang, Liwenying Li, Ming |
| contents | By introducing a simple competition mechanism for bond insertion in random graphs, explosive percolation exhibits a sharp phase transition with rich critical phenomena. We investigate high-order connectivity in explosive percolation using an event-based ensemble, focusing on biconnected clusters, where any two sites are connected by at least two independent paths. Our numerical analysis confirms that explosive percolation with different intra-cluster bond competition rules shares the same percolation threshold and universality, with biconnected clusters percolating simultaneously with simply connected clusters. However, the volume fractal dimension $d_{f}'$ of biconnected clusters varies depending on the competition rules of intra-cluster bonds. The size distribution of biconnected clusters exhibits double-scaling behavior: large clusters follow the standard Fisher exponent derived from the hyperscaling relation $τ'=1+1/d_{f}'$, while small clusters display a modified Fisher exponent $τ_0<τ'$. These findings provide insights into the intricate nature of connectivity in explosive percolation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02789 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Emergence of biconnected clusters in explosive percolation Yang, Liwenying Li, Ming Statistical Mechanics By introducing a simple competition mechanism for bond insertion in random graphs, explosive percolation exhibits a sharp phase transition with rich critical phenomena. We investigate high-order connectivity in explosive percolation using an event-based ensemble, focusing on biconnected clusters, where any two sites are connected by at least two independent paths. Our numerical analysis confirms that explosive percolation with different intra-cluster bond competition rules shares the same percolation threshold and universality, with biconnected clusters percolating simultaneously with simply connected clusters. However, the volume fractal dimension $d_{f}'$ of biconnected clusters varies depending on the competition rules of intra-cluster bonds. The size distribution of biconnected clusters exhibits double-scaling behavior: large clusters follow the standard Fisher exponent derived from the hyperscaling relation $τ'=1+1/d_{f}'$, while small clusters display a modified Fisher exponent $τ_0<τ'$. These findings provide insights into the intricate nature of connectivity in explosive percolation. |
| title | Emergence of biconnected clusters in explosive percolation |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2403.02789 |