Oslo model, hyperuniformity, and the quenched Edwards-Wilkinson model.

Area of Science:

• Complex Systems
• Statistical Physics
• Computational Physics

Background:

• The 1D Oslo rice pile model is a fundamental sand-pile model.
• Previous simulations suffered from significant finite-size corrections, limiting accuracy.
• Understanding the model's stationary state and critical behavior is crucial.

Purpose of the Study:

• To accurately simulate the 1D Oslo rice pile model using its hyperuniform stationary state.
• To determine precise values for critical exponents, overcoming finite-size limitations.
• To explore the relationship between hyperuniformity and correlation length, and connections to other models.

Main Methods:

• Simulations of the 1D Oslo rice pile model with random critical height resetting.
• Leveraging the hyperuniformity of the stationary state for large system sizes (>10^7).
• Analysis of critical exponents (correlation length, fractal dimension, dynamical exponent) and roughness exponents.

Main Results:

• Precise rational values for critical exponents: ν=4/3, D=9/4, z=10/7.
• Established a relationship between the hyperuniformity exponent and the correlation length exponent ν.
• Found the local roughness exponent α_loc=1 in relation to the quenched Edwards-Wilkinson model.

Conclusions:

• The hyperuniformity of the 1D Oslo rice pile model enables highly accurate simulations.
• Critical exponents are consistent with simple rational numbers, providing a refined understanding.
• The study clarifies connections between sand-pile models, hyperuniformity, and surface growth models.