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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.00120 |
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| _version_ | 1866910284768083968 |
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| author | Zhang, Yongwen Liu, Maoxin Hu, Gaoke Liu, Teng Chen, Xiaosong |
| author_facet | Zhang, Yongwen Liu, Maoxin Hu, Gaoke Liu, Teng Chen, Xiaosong |
| contents | We employ the eigen microstate approach to explore the self-organized criticality (SOC) in two celebrated sandpile models, namely, the BTW model and the Manna model. In both models, phase transitions from the absorbing-state to the critical state can be understood by the emergence of dominant eigen microstates with significantly increased weights. Spatial eigen microstates of avalanches can be uniformly characterized by a linear system size rescaling. The first temporal eigen microstates reveal scaling relations in both models. Furthermore, by finite-size scaling analysis of the first eigen microstate, we numerically estimate critical exponents i.e., $\sqrt{σ_0 w_1}/\tilde{v}_{1} \propto L^D$ and $\tilde{v}_{1} \propto L^{D(1-τ_s)/2}$. Our findings could provide profound insights into eigen states of the universality and phase transition in non-equilibrium complex systems governed by self-organized criticality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00120 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Eigenstates in the self-organised criticality Zhang, Yongwen Liu, Maoxin Hu, Gaoke Liu, Teng Chen, Xiaosong Physics and Society Statistical Mechanics We employ the eigen microstate approach to explore the self-organized criticality (SOC) in two celebrated sandpile models, namely, the BTW model and the Manna model. In both models, phase transitions from the absorbing-state to the critical state can be understood by the emergence of dominant eigen microstates with significantly increased weights. Spatial eigen microstates of avalanches can be uniformly characterized by a linear system size rescaling. The first temporal eigen microstates reveal scaling relations in both models. Furthermore, by finite-size scaling analysis of the first eigen microstate, we numerically estimate critical exponents i.e., $\sqrt{σ_0 w_1}/\tilde{v}_{1} \propto L^D$ and $\tilde{v}_{1} \propto L^{D(1-τ_s)/2}$. Our findings could provide profound insights into eigen states of the universality and phase transition in non-equilibrium complex systems governed by self-organized criticality. |
| title | Eigenstates in the self-organised criticality |
| topic | Physics and Society Statistical Mechanics |
| url | https://arxiv.org/abs/2401.00120 |