Logarithmic corrections of the avalanche distributions of sandpile models at the upper critical dimension

Abstract

We study numerically the dynamical properties of the BTW model on a square lattice for various dimensions. The aim of this investigation is to determine the value of the upper critical dimension where the avalanche distributions are characterized by the mean-field exponents. Our results are consistent with the assumption that the scaling behavior of the four-dimensional BTW model is characterized by the mean-field exponents with additional logarithmic corrections. We benefit in our analysis from the exact solution of the directed BTW model at the upper critical dimension which allows to derive how logarithmic corrections affect the scaling behavior at the upper critical dimension. Similar logarithmic corrections forms fit the numerical data for the four-dimensional BTW model, strongly suggesting that the value of the upper critical dimension is four.

8 pages, including 9 figures, accepted for publication in Phys. Rev. E

References in corpus (4)

• Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model
• The Bak-Tang-Wiesenfeld sandpile model around the upper critical dimension
• Mean-field behavior of the sandpile model below the upper critical dimension
• Symmetries and Fixed Point Stability of Stochastic Differential Equations Modeling Self-Organized Criticality

Cited by in corpus (12)

• The abelian sandpile and related models
• Driving, conservation and absorbing states in sandpiles
• Scaling of waves in the Bak-Tang-Wiesenfeld sandpile model
• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• Universality classes in directed sandpile models
• Critical and Near-Critical Branching Processes
• Critical behavior and conservation in directed sandpiles
• Universal scaling behavior of directed percolation around the upper critical dimension
• Disorder-induced phase transition in a one-dimensional model of rice pile
• Directed Abelian sandpile with multiple downward neighbors
• Absorbing phase transitions in a non-conserving sandpile model
• Kinetic description of avalanching systems