Eigen microstates in self-organized criticality.

Area of Science:

• Complex Systems
• Statistical Physics
• Non-equilibrium Dynamics

Background:

• Self-organized criticality (SOC) describes complex systems that naturally evolve to a critical state.
• Sandpile models, like the BTW and Manna models, are canonical examples used to study SOC phenomena.
• Understanding phase transitions in these systems is crucial for characterizing their emergent behavior.

Purpose of the Study:

• To explore self-organized criticality (SOC) in the BTW and Manna sandpile models using the eigen microstates approach.
• To characterize the emergence of dominant eigen microstates during phase transitions.
• To numerically estimate critical exponents associated with these transitions.

Main Methods:

• Application of the eigen microstates approach to analyze sandpile models.
• Characterization of spatial eigen microstates using linear system size rescaling.
• Analysis of temporal eigen microstates and their scaling relations.
• Finite-size scaling analysis to estimate critical exponents.

Main Results:

• Emergence of dominant eigen microstates signifies phase transitions from absorbing to critical states.
• Spatial eigen microstates exhibit uniform characterization via system size rescaling.
• First temporal eigen microstates demonstrate scaling relations in both models.
• Numerical estimation of critical exponents, including D and τs, using finite-size scaling.

Conclusions:

• The eigen microstates approach provides a unified framework for understanding phase transitions in SOC systems.
• Findings offer profound insights into the universality and critical behavior of non-equilibrium complex systems.
• The study highlights the significance of eigen microstates in characterizing emergent phenomena in sandpile models.