Related papers: Numerical simulations of directed sandpile models
We consider disordered systems of directed polymer type, for which disorder is so-called marginally relevant. These include the usual (short-range) directed polymer model in dimension (2+1), the long-range directed polymer model with Cauchy…
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…
The universality of the directed polymer model and the analogous KPZ equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three and four dimensions. It is shown that although in the…
With a toppling rule which generates metastable sites, we explore the properties of a gradient-driven sandpile that is minimally perturbed at one boundary. In two dimensions we find that the transport of grains takes place along deep…
Can the concept of self-organized criticality, exemplified by models such as the sandpile model, be described within the framework of continuous phase transitions? In this paper, we provide extensive numerical evidence supporting an…
Rotational constraint representing a local external bias generally has non-trivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in a out of…
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…
The dynamics of sandpile models are mapped to discrete interface equations. We study in detail the Bak-Tang-Wiesenfeld model, a stochastic model with random thresholds, and the Manna model. These are, respectively, discretizations of the…
We have studied one-dimensional cellular automata with updating rules depending stochastically on the difference of the heights of neighbouring cells. The probability for toppling depends on a parameter lambda which goes to one with…
We consider the stochastic sandpile model with uniform toppling rule on the integer line. During a uniform toppling, with probability $1/3$ one particle is sent to the right of the toppled vertex, with probability $1/3$ one particle is sent…
We study universality classes and crossover behaviors in non-Abelian directed sandpile models, in terms of the metastable pattern analysis. The non-Abelian property induces spatially correlated metastable patterns, characterized by the…
Physical understanding of how the interplay between symmetries and nonlinear effects can control the scaling and multiscaling properties in a coupled driven system, such as magnetohydrodynamic turbulence or turbulent binary fluid mixtures,…
We provide a comprehensive view on the role of Abelian symmetry and stochasticity in the universality class of directed sandpile models, in context of the underlying spatial correlations of metastable patterns and scars. It is argued that…
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…
In the past many papers have appeared which simulated surface growth with different growth models. The results showed that, if models differed only slightly in their `growth' rules, the resulting surfaces may belong to different…
I report large-scale Monte Carlo studies of a one-dimensional height-restricted stochastic sandpile using the quasistationary simulation method. Results for systems of up to 50 000 sites yield estimates for critical exponents that differ…
Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
We solve a long-standing puzzle in Statistical Mechanics of disordered systems. By performing a high-statistics simulation of the D=3 random-field Ising model at zero temperature for different shapes of the random-field distribution, we…
Fixed-energy sandpiles with stochastic update rules are known to exhibit a nonequilibrium phase transition from an active phase into infinitely many absorbing states. Examples include the conserved Manna model, the conserved lattice gas,…
Sandpile models with conserved number of particles (also called fixed energy sandpiles) may undergo phase transitions between active and absorbing states. We generalize the Manna sandpile model with fixed number of particles, introducing a…