Related papers: Exact solutions for a mean-field Abelian sandpile
Adding grains at a single site on a flat substrate in the Abelian sandpile models produce beautiful complex patterns. We study in detail the pattern produced by adding grains on a two-dimensional square lattice with directed edges (each…
We perform a high-accuracy moment analysis of the avalanche size, duration and area distribution of the Abelian Manna model on eight two-dimensional and four one-dimensional lattices. The results provide strong support to establish…
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated to the probability density of oscillators with a given…
For a driven elastic object near depinning, we derive from first principles the distribution of instantaneous velocities in an avalanche. We prove that above the upper critical dimension, d >= d_uc, the n-times distribution of the…
Kinetic self-avoiding trails are introduced and used to generate a substrate of randomly quenched flow vectors. Sandpile model is studied on such a substrate with asymmetric toppling matrices where the precise balance between the net…
The Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. The dynamics of the sandpiles occur when the grains topple over a graph. In this study, we allow the graph to evolve…
We investigate the avalanche dynamics of the abelian sandpile model on arbitrarily large balls of the expanded cactus graph (the Cayley graph of the free product $\mathbb{Z}_3 * \mathbb{Z}_2$). We follow the approach of Dhar and Majumdar…
We show that a fixed set of woven defect lines in a nematic liquid crystal supports a set of non-singular topological states which can be mapped on to recurrent stable configurations in the Abelian sandpile model or chip-firing game. The…
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…
We introduce a class of discrete models for surface relaxation. By exactly solving the master equation which governs the microscopic dynamics of the surface, we determine the steady state of the surface and calculate its roughness. We will…
The aim of this note is to systematize our knowledge about identical configurations of ASM.
We give a comprehensive self-contained review on the rigorous analysis of the thermodynamics of a class of random spin systems of mean field type whose most prominent example is the Hopfield model. We focus on the low temperature phase and…
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…
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…
We study the geometrical structure of the states in the low temperature phase of a mean field model for generalized spin glasses, the p-spin spherical model. This structure cannot be revealed by the standard methods, mainly due to the…
Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…
The main result of this paper is a rigorous proof of criticality and an explicit computation of critical exponents for the decay of avalanches in the Abelian sandpile model (ASM) on a large family of infinite graphs. We begin by introducing…
We study a random fiber bundle model with tips of the fibers placed on a graph having co-ordination number 3. These fibers follow local load sharing with uniformly distributed threshold strengths of the fibers. We have studied the critical…
Within the replica approach to mean-field spin-glasses the transition from ergodic high-temperature behaviour to the glassy low-temperature phase is marked by the instability of the replica-symmetric saddle-point. For general spin-glass…
We consider an interacting particle system $(\eta_t)_{t\geq 0}$ with values in $\{0,1\}^{\mathbb{Z}}$, in which each vacant site becomes occupied with rate 1, while each connected component of occupied sites become vacant with rate equal to…