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The notion of Self-organized criticality (SOC) had been conceived to interpret the spontaneous emergence of long range correlations in nature. Since then many different models had been introduced to study SOC. All of them have few common…

Statistical Mechanics · Physics 2023-05-03 S. S. Manna

We study a nonconservative sandpile model in one dimension, in which, if the height at any site exceeds a threshold value, the site topples by transferring one particle along each bond connecting it to its neighbours. Its height is then set…

Condensed Matter · Physics 2016-08-31 Agha Afsar Ali

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…

Mathematical Physics · Physics 2017-06-19 J. P. Keating , N. Linden , H. J. Wells

We revisit the sandpile model with ``sticky'' grains introduced by Mohanty and Dhar [Phys. Rev. Lett. {\bf 89}, 104303 (2002)] whose scaling properties were claimed to be in the universality class of directed percolation for both isotropic…

Statistical Mechanics · Physics 2009-11-11 Juan A. Bonachela , Jose J. Ramasco , Hugues Chate , Ivan Dornic , Miguel A. Munoz

We study the creep response of solids to a constant external load in the framework of a novel fiber bundle model introduced. Analytical and numerical calculations showed that increasing the external load on a specimen a transition takes…

Statistical Mechanics · Physics 2007-05-23 Ferenc Kun , Yamir Moreno , Raul Cruz Hidalgo , Hans. J. Herrmann

We consider the abelian stochastic sandpile model. In this model, a site is deemed unstable when it contains more than one particle. Each unstable site, independently, is toppled at rate $1$, sending two of its particles to neighbouring…

Probability · Mathematics 2021-03-17 Moumanti Podder , Leonardo T. Rolla

We present simulations of the 1-dimensional Oslo rice pile model in which the critical height at each site is randomly reset after each toppling. We use the fact that the stationary state of this sandpile model is hyperuniform to reach…

Statistical Mechanics · Physics 2016-11-02 Peter Grassberger , Deepak Dhar , P. K. Mohanty

We study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the…

Statistical Mechanics · Physics 2009-10-31 Maya Paczuski , Kevin E. Bassler

Using renormalized field theory, we examine the dynamics of a growing surface, driven by an obliquely incident particle beam. Its projection on the reference (substrate) plane selects a ``parallel'' direction, so that the evolution equation…

Statistical Mechanics · Physics 2009-11-11 B. Schmittmann , Gunnar Pruessner , H. K. Janssen

The Oslo rice pile model is a sandpile-like paradigmatic model of ``Self-Organized Criticality'' (SOC). In this paper it is shown that the Oslo model is in fact exactly a discrete realization of the much studied quenched Edwards-Wilkinson…

Statistical Mechanics · Physics 2009-11-07 Gunnar Pruessner

In the rotational sandpile model, either the clockwise or the anti-clockwise toppling rule is assigned to all the lattice sites. It has all the features of a stochastic sandpile model but belongs to a different universality class than the…

Statistical Mechanics · Physics 2015-01-09 Himangsu Bhaumik , Jahir Abbas Ahmed , S. B. Santra

It was recently found that the classical 3d O$(N)$ model in the semi-infinite geometry can exhibit an "extraordinary-log" boundary universality class, where the spin-spin correlation function on the boundary falls off as $\langle \vec{S}(x)…

Strongly Correlated Electrons · Physics 2024-08-26 Abijith Krishnan , Max A. Metlitski

The Abelian Sandpile Model is a discrete diffusion process defined on graphs (Dhar \cite{DD90}, Dhar et al. \cite{DD95}) which serves as the standard model of self-organized criticality. The transience class of a sandpile is defined as the…

Discrete Mathematics · Computer Science 2012-11-02 Ayush Choure , Sundar Vishwanathan

Multiple avalanches, initiated by simultaneously toppling neighbouring sites, are studied in three different directed sandpile models. It is argued that, while the single avalanche exponents are different for the three models, a suitably…

Statistical Mechanics · Physics 2011-05-13 R. Rajesh

We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the…

Probability · Mathematics 2018-05-23 Achillefs Tzioufas

In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling…

Statistical Mechanics · Physics 2009-11-11 S. Lubeck , R. D. Willmann

In the single-source sandpile model, a number $N$ grains of sand are positioned at a central vertex on the 2-dimensional grid $\mathbb{Z}^2$. We study the stabilisation of this configuration for a stochastic sandpile model based on a…

Probability · Mathematics 2022-08-23 Thomas Selig , Haoyue Zhu

Two-component sandpile models are investigated numerically and theoretically. Monte Calro simulations are performed to show that probability distribution functions of avalanche size and lifetime obey power laws whose exponents are…

Statistical Mechanics · Physics 2007-05-23 Akihiro Fujihara , Toshiya Ohtsuki , Teruhiro Nakagawa

We discuss various critical densities in sandpile models. The stationary density is the average expected height in the stationary state of a finite-volume model; the transition density is the critical point in the infinite-volume…

Mathematical Physics · Physics 2012-11-21 Anne Fey , Ronald Meester

We investigate the critical behavior of systems exhibiting a continuous absorbing phase transition in the presence of a conserved field coupled to the order parameter. The results obtained point out the existence of a new universality class…

Statistical Mechanics · Physics 2009-10-31 Michela Rossi , Romualdo Pastor-Satorras , Alessandro Vespignani