Correlation, crossover and broken scaling in the Abelian Manna Model

2023/11/06 by Chen, Letian, Huynh, Hoai Nguyen, Pruessner, Gunnar
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2311.03513

Abstract

The role of correlations in self-organised critical (SOC) phenomena is investigated by studying the Abelian Manna Model (AMM) in two dimensions. Local correlations of the debris left behind after avalanches are destroyed by re-arranging particles on the lattice between avalanches, without changing the one-point particle density. It is found that the spatial correlations are not relevant to small avalanches, while changing the scaling of the large (system-wide) ones, yielding a crossover in the model's scaling behaviour. This crossover breaks the simple scaling observed in normal SOC.

Related

• Spatio-temporal Correlations in the Manna Model in one, three and five dimensions
• The average avalanche size in the Manna Model and other models of self-organised criticality
• Non-Abelian self-organized criticality model with one stochastic site in any avalanche shows multifractal scaling
• Breakdown of the Universality Hypothesis in Directed Abelian Sandpile\n Models
• Self-organised dynamics beyond scaling of avalanches: Cyclic stress fluctuations in critical sandpiles