Extra investigation of the self-organized critical Manna model at higher critical dimension

A. V. Podlazov


Abstract: I investigate the nature of the upper critical dimension for isotropic conservative sandpile models and calculate the emerging logarithmic corrections to power-law distributions. I check the results experimentally using the case of Manna model with the theoretical solution known for all statement starting from the two-dimensional one. In addition, based on this solution, I construct a non-trivial super-universal indicator for this model. It characterizes the distribution of avalanches by time the border of their region needs to pass its width.

Keywords: self-organized criticality, sandpiles, Manna model, scale invariance, power laws, logarithmic corrections, upper critical dimension, super-universal indices.

DOI: 10.20948/prepr-2021-76