Eigenstates in the self-organised criticality

2023/12/30 by Yongwen Zhang, Zhang, Yongwen, Maoxin Liu +7
Materials Science · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Physical sciences #Material Dynamics and Properties #Physics and Society (physics.soc-ph) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2401.00120

openalex publication_date 2023/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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., √(σ₀ w₁)/v₁ ∝ L^D and v₁ ∝ 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.

Related

• Self-organized criticality as a phase transition
• Describing Self-organized Criticality as a continuous phase transition
• Self-organised dynamics beyond scaling of avalanches: Cyclic stress fluctuations in critical sandpiles
• Avalanche Behavior in an Absorbing State Oslo Model
• Condensation of Eigen Microstate in Statistical Ensemble and Phase Transition