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1997

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/18804

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

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http://dx.doi.org/10.1103/PhysRevE.55.2434

Abstract

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Subject

Física estadística, Termodinàmica, Sistemes no lineals, Propietats magnètiques, Equacions d'estat, Regla de les fases i equilibri, Transformacions de fase (Física estadística), Equacions diferencials estocàstiques

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Statistical physics, Thermodynamics, Nonlinear systems, Magnetic properties, Equations of state, Phase rule and equilibrium, Phase transformations (Statistical physics), Stochastic differential equations

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Articles publicats en revistes (Física de la Matèria Condensada)

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CORRAL, Álvaro and DÍAZ GUILERA, Albert. Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality. Physical Review E. 1997. Vol. 55, num. 3, pags. 2434-2445. ISSN 1063-651X. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/18804

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