Universal Scaling of Gap Dynamics in Percolation
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916463446589440 |
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| author | Fang, Sheng Lin, Qing Meng, Jun Chen, Bingsheng Nagler, Jan Deng, Youjin Fan, Jingfang |
| author_facet | Fang, Sheng Lin, Qing Meng, Jun Chen, Bingsheng Nagler, Jan Deng, Youjin Fan, Jingfang |
| contents | Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest cluster across various percolation models, spanning from latticebased to network systems, encompassing both continuous and discontinuous percolation. Our results uncover an inherent self-similarity in the dynamical process both for critical and supercritical phase, characterized by two independent Fisher exponents, respectively. Utilizing a scaling ansatz, we propose a novel scaling relation that links the discovered Fisher exponents with other known critical exponents. Additionally, we demonstrate the application of our theory to real systems, showing its practical utility in extracting the corresponding Fisher exponents. These findings enrich our understanding of percolation dynamics and highlight the robust and universal scaling laws that transcend individual models and extend to broader classes of complex systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal Scaling of Gap Dynamics in Percolation Fang, Sheng Lin, Qing Meng, Jun Chen, Bingsheng Nagler, Jan Deng, Youjin Fan, Jingfang Statistical Mechanics Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest cluster across various percolation models, spanning from latticebased to network systems, encompassing both continuous and discontinuous percolation. Our results uncover an inherent self-similarity in the dynamical process both for critical and supercritical phase, characterized by two independent Fisher exponents, respectively. Utilizing a scaling ansatz, we propose a novel scaling relation that links the discovered Fisher exponents with other known critical exponents. Additionally, we demonstrate the application of our theory to real systems, showing its practical utility in extracting the corresponding Fisher exponents. These findings enrich our understanding of percolation dynamics and highlight the robust and universal scaling laws that transcend individual models and extend to broader classes of complex systems. |
| title | Universal Scaling of Gap Dynamics in Percolation |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2410.24068 |