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An action with $n$ parameters, which generalizes the $O(N) - R P^{N-1}$ -model, is considered in one dimension for general $N$. We use asymptotic expansion techniques to determine where the model becomes critical and show that for the…

High Energy Physics - Lattice · Physics 2009-10-28 Erhard Seiler , Karim Yildirim

We introduce a one-dimensional sandpile model with $N$ different particle types and an infinitesimal driving rate. The parameters for the model are the N^2 critical slopes for one type of particle on top of another. The model is trivial…

Statistical Mechanics · Physics 2009-10-30 D. A. Head , G. J. Rodgers

Sand pile models are dynamical systems describing the evolution from $N$ stacked grains to a stable configuration. It uses local rules to depict grain moves and iterate it until reaching a fixed configuration from which no rule can be…

Discrete Mathematics · Computer Science 2013-02-19 Kévin Perrot , Eric Rémila

We present a unified mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF)…

Statistical Mechanics · Physics 2009-10-30 Alessandro Vespignani , Stefano Zapperi

We introduce a one-dimensional sandpile model which incorporates particle inertia. The inertial dynamics are governed by a new parameter which, as it passes through a threshold value, alters the toppling dynamics in such a way that the…

Condensed Matter · Physics 2009-10-28 D. A. Head , G. J. Rodgers

Using the transfer matrix method, we give the exact solution of a deterministic sandpile model for arbitrary $N$, where $N$ is the size of a single toppling. The one- and two-point functions are given in term of the eigenvalues of an $N…

Condensed Matter · Physics 2009-10-28 Darwin Chang , Shih-Chang Lee , Wen-Jer Tzeng

A two state sandpile model with preferential sand distribution is developed and studied numerically on scale free networks with power-law degree ($k$) distribution, {\em i.e.}: $P_k\sim k^{-\alpha}$. In this model, upon toppling of a…

Statistical Mechanics · Physics 2017-05-31 Himangsu Bhaumik , S. B. Santra

We show that in a broad class of directed abelian sandpile models that had been expected to have the same exponents as the Dhar-Ramaswamy model, the avalanche exponent depends upon the details of the interaction, calling into question the…

Condensed Matter · Physics 2007-05-23 Rick Tully , George Reiter

We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around…

Statistical Mechanics · Physics 2009-11-10 R. Karmakar , S. S. Manna

We study a restricted-height version of the one-dimensional Oslo sandpile with conserved density, using periodic boundary conditions. Each site has a limiting height which can be either two or three. When a site reaches its limiting height…

Statistical Mechanics · Physics 2015-11-09 Vanuildo Silva de Carvalho , Alvaro de Almeida Caparica , Ronald Dickman

We study sandpile models as closed systems, with conserved energy density $\zeta$ playing the role of an external parameter. The critical energy density, $\zeta_c$, marks a nonequilibrium phase transition between active and absorbing…

Statistical Mechanics · Physics 2016-08-31 Alessandro Vespignani , Ronald Dickman , Miguel A. Munoz , Stefano Zapperi

A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation. This theory predicts that the stationary density of the abelian sandpile model equals the threshold density of the fixed-energy…

Statistical Mechanics · Physics 2010-06-10 Anne Fey , Lionel Levine , David B. Wilson

Sandpiles form one of the largest class of models displaying a critical stationary state. Despite a few decades of research, a comprehensive and systematic rigorous characterisation of their spatial and, even more, time dependent properties…

Statistical Mechanics · Physics 2025-12-23 Valentin Lallemant

The divisible sandpile model is a fixed-energy continuous counterpart of the Abelian sandpile model. We start with a random initial configuration and redistribute mass deterministically. Under certain conditions the sandpile will stabilize.…

Probability · Mathematics 2019-10-16 Wioletta M. Ruszel

We consider the nonabelian sandpile model defined on directed trees by Ayyer, Schilling, Steinberg and Thi\'ery (Commun. Math. Phys, 2013) and restrict it to the special case of a one-dimensional lattice of $n$ sites which has open…

Statistical Mechanics · Physics 2016-03-04 Arvind Ayyer

Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of Self-Organized Criticality. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain…

Discrete Mathematics · Computer Science 2012-07-04 Kevin Perrot , Thi Ha Duong Phan , Trung Van Pham

The precise determination of the universality classes in self-organized critical phenomena (SOC) is still an unsolved problem. Different SOC models like sandpile, linear interface depinning, and the Barkhausen effect have been investigated…

Condensed Matter · Physics 2007-05-23 Alexei Vazquez , Oscar Sotolongo-Costa

We use a phenomenological field theory, reflecting the symmetries and conservation laws of sandpiles, to compare the driven dissipative sandpile, widely studied in the context of self-organized criticality, with the corresponding…

Statistical Mechanics · Physics 2009-10-31 Alessandro Vespignani , Ronald Dickman , Miguel A. Munoz , Stefano Zapperi

A single sandpile model with quenched random toppling matrices captures the crucial features of different models of self-organized criticality. With symmetric matrices avalanche statistics falls in the multiscaling BTW universality class.…

Statistical Mechanics · Physics 2009-11-10 R. Karmakar , S. S. Manna , A. L. Stella

We show that any amount of anisotropy moves the Oslo model to another known universality class, the exponents of which can be derived exactly. This amounts to an exact solution of the quenched Edwards-Wilkinson equation with a drift term.…

Statistical Mechanics · Physics 2007-05-23 Gunnar Pruessner , Henrik Jeldtoft Jensen