Abstract
The Manna model—the conservative isotropic self-organized critical sandpile model—is studied. The results of computer simulation in two-, three-, and four-dimensional formulations, as well as an analytical solution for space dimensions between the lower and upper critical dimensions, are presented for this model. The solution is based on the construction of a mesolevel model formulated in terms of the excitation density, its correlation length, and the average activity and the boundary width of the avalanche region. The indices are calculated by two independent methods: on the basis of the renormalization of stochastic differential equations and by reducing the occurring processes to random walks.
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Podlazov, A.V. Solution of the Self-Organized Critical Manna Model in Space Dimensions 2 to 4. J. Exp. Theor. Phys. 134, 350–363 (2022). https://doi.org/10.1134/S1063776122030104
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DOI: https://doi.org/10.1134/S1063776122030104