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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.17376 |
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| _version_ | 1866912208606199808 |
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| author | Manna, S. S. |
| author_facet | Manna, S. S. |
| contents | Can the concept of self-organized criticality, exemplified by models such as the sandpile model,
be described within the framework of continuous phase transitions? In this paper, we provide extensive
numerical evidence supporting an affirmative answer. Specifically, we explore the BTW and Manna sandpile
models as instances of percolation transitions from disordered to ordered phases. To facilitate this
analysis, we introduce the concept of drop density, a continuously adjustable control variable that
quantifies the average number of particles added to a site. By tuning this variable, we observe a
transition in the sandpile from a sub-critical to a critical phase. Additionally, we define the scaled size
of the largest avalanche occurring from the beginning of the sandpile as the order parameter for the
self-organized critical transition and analyze its scaling behavior. Furthermore, we calculate the
correlation length exponent and note its divergence as the critical point is approached. The finite
size scaling analysis of the avalanche size distribution works quite well at the critical point of the
BTW sandpile. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17376 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Describing Self-organized Criticality as a continuous phase transition Manna, S. S. Statistical Mechanics Can the concept of self-organized criticality, exemplified by models such as the sandpile model, be described within the framework of continuous phase transitions? In this paper, we provide extensive numerical evidence supporting an affirmative answer. Specifically, we explore the BTW and Manna sandpile models as instances of percolation transitions from disordered to ordered phases. To facilitate this analysis, we introduce the concept of drop density, a continuously adjustable control variable that quantifies the average number of particles added to a site. By tuning this variable, we observe a transition in the sandpile from a sub-critical to a critical phase. Additionally, we define the scaled size of the largest avalanche occurring from the beginning of the sandpile as the order parameter for the self-organized critical transition and analyze its scaling behavior. Furthermore, we calculate the correlation length exponent and note its divergence as the critical point is approached. The finite size scaling analysis of the avalanche size distribution works quite well at the critical point of the BTW sandpile. |
| title | Describing Self-organized Criticality as a continuous phase transition |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2501.17376 |