Critical density of the Abelian Manna model via a multitype branching process
| Autor: | Gunnar Pruessner, Nanxin Wei |
|---|---|
| Přispěvatelé: | Engineering and Physical Sciences Research Council |
| Rok vydání: | 2019 |
| Předmět: |
Phase transition
Science & Technology Statistical Mechanics (cond-mat.stat-mech) Physics SELF-ORGANIZED CRITICALITY FOS: Physical sciences 01 natural sciences Self-organized criticality 010305 fluids & plasmas Universality (dynamical systems) Physics Mathematical Physics Fluids & Plasmas Physical Sciences 0103 physical sciences PHASE-TRANSITIONS UNIVERSALITY SANDPILE Statistical physics Abelian group 010306 general physics Condensed Matter - Statistical Mechanics Mathematics Branching process |
| Zdroj: | Physical Review E. 100 |
| ISSN: | 2470-0053 2470-0045 |
| Popis: | A multi-type branching process is introduced to mimic the evolution of the avalanche activity and determine the critical density of the Abelian Manna model. This branching process incorporates partially the spatio-temporal correlations of the activity, which are essential for the dynamics, in particular in low dimensions. An analytical expression for the critical density in arbitrary dimensions is derived, which significantly improves the results over mean-field theories, as confirmed by comparison to the literature on numerical estimates from simulations. The method can easily be extended to lattices and dynamics other than those studied in the present work. Comment: 5 pages, 2 figures, 2 tables |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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