Related papers: Scaling laws and simulation results for the self--…

We discuss the scaling behavior of the self-organized critical forest-fire model on large length scales. As indicated in earlier publications, the forest-fire model does not show conventional critical scaling, but has two qualitatively…

We modify the rules of the self-organized critical forest-fire model in one dimension by allowing the fire to jump over holes of $\le k$ sites. An analytic calculation shows that not only the size distribution of forest clusters but also…

We present the analytic solution of the self-organized critical (SOC) forest-fire model in one dimension proving SOC in systems without conservation laws by analytic means. Under the condition that the system is in the steady state and very…

We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of…

We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two-point correlation function of trees.…

Depending on the rule for tree growth, the forest-fire model shows either self-organized criticality with rule-dependent exponents, or synchronization, or an intermediate behavior. This is shown analytically for the one-dimensional system,…

The forest fire model is a reaction-diffusion model where energy, in the form of trees, is injected uniformly, and burned (dissipated) locally. We show that the spatial distribution of fires forms a novel geometric structure where the…

We present a systematic study of corrections to scaling in the self-organized critical forest-fire model. The analysis of the steady-state condition for the density of trees allows us to pinpoint the presence of these corrections, which…

We include immunity against fire as a new parameter into the self-organized critical forest-fire model. When the immunity assumes a critical value, clusters of burnt trees are identical to percolation clusters of random bond percolation. As…

We reconsider a model introduced by Bak, Chen, and Tang (Phys. Rev. A 38, 364 (1988)) as a supposedly self-organized critical model for forest fires. We verify again that the model is not critical in 2 dimensions, as found also by previous…

The one-dimensional forest-fire model including lightnings is studied numerically and analytically. For the tree correlation function, a new correlation length with critical exponent \nu ~ 5/6 is found by simulations. A Hamiltonian…

We study finite-size effects in the self-organized critical forest-fire model by numerically evaluating the tree density and the fire size distribution. The results show that this model does not display the finite-size scaling seen in…

We show by extensive simulations that the whole supercritical phase of the three-dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of critical phenomena. Besides typical scalings like algebraically…

Ecological communities exhibit pervasive patterns and inter-relationships between size, abundance, and the availability of resources. We use scaling ideas to develop a unified, model-independent framework for understanding the distribution…

There are two independent critical exponents that describe the behavior of systems near their critical point. However, at the critical point only the exponent $\eta$, which describes the decay of the correlation function, is usually…

We demonstrate the emergence of scaling laws in the benchmark top versus QCD jet classification problem in collider physics. Six distinct physically-motivated classifiers exhibit power-law scaling of the binary cross-entropy test loss as a…

We consider a forest-fire model which, somewhat informally, is described as follows: Each site (vertex) of the square lattice is either vacant or occupied by a tree.Vacant sites become occupied at rate 1. Further, each site is hit by…

In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…

We analyse numerically the critical behavior of an absorbing phase transition in a conserved lattice gas in an external field. The external field is realized as a spontaneous creation of active particles which drives the system away from…

Critical, or scale independent, systems are so ubiquitous, that gaining theoretical insights on their nature and properties has many direct repercussions in social and natural sciences. In this report, we start from the simplest possible…