Multiplicative Renormalization of Stochastic Differential Equations for the Abelian Sandpile Model

Date

2024

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Abstract

The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling parameters, calculate an infinite number of renormalization constants, identify a plane of fixed points in the infinite dimensional space of coupling parameters, discuss their stability and critical scaling in the model, and formulate a simple law relating the asymptotic size of an avalanche to a model exponent quantifying the time-scale separation between the slow energy injection and fast avalanche relaxation processes.

Description

© 2024 by the author. cc-by

Keywords

critical scaling, multiplicative renormalization, self-organized criticality

Citation

Volchenkov, D.. 2024. Multiplicative Renormalization of Stochastic Differential Equations for the Abelian Sandpile Model. Dynamics, 4(1). https://doi.org/10.3390/dynamics4010003

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