相关论文: Broken scaling in the Forest Fire Model

We introduce a novel approach to study the critical behavior of equilibrium and non-equilibrium systems which is based on the concept of an instantaneous correlation length. We analyze in detail two classical statistical mechanical systems:…

Globally conserved interface-controlled coarsening of fractal clusters exhibits dynamic scale invariance and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The…

In the distributed burning regime, turbulence disrupts the internal structure of the flame, and so the idea of laminar burning propagated by conduction is no longer valid. The nature of the burning depends on the turbulent Damkohler number…

Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity…

We consider the so-called one-dimensional forest fire process. At each site of $\mathbb{Z}$, a tree appears at rate $1$. At each site of $\mathbb{Z}$, a fire starts at rate ${\lambda}>0$, immediately destroying the whole corresponding…

A geometric approach to critical fluctuations of a nonequilibrium model is reported. The two-dimensional majority vote model was investigated by Monte Carlo simulations on square lattices of various sizes and a detailed scaling analysis of…

Scaling laws in astrophysical systems that involve the energy, the geometry, and the spatio-temporal evolution, provide the theoretical framework for physical models of energy dissipation processes. A leading model is the standard…

We perform a systematic analysis of an extension of the Standard Model that includes a complex singlet scalar field and is scale invariant at the tree level. We call such a model the Minimal Scale Invariant extension of the Standard Model…

The N\'eel temperature, staggered magnetization density, as well as the spinwave velocity of a three-dimensional (3D) quantum Heisenberg model with antiferromagnetic disorder (randomness) are calculated using first principles…

We discuss the scaling properties of free branched polymers. The scaling behaviour of the model is classified by the Hausdorff dimensions for the internal geometry: d_L and d_H, and for the external one: D_L and D_H. The dimensions d_H and…

We consider the morphology of two dimensional cracks observed in experimental results obtained from paper samples and compare these results with the numerical simulations of the random fuse model (RFM). We demonstrate that the data obey…

Within the numerically exact solution to the Dicke model proposed previously, we study the quantum criticality in terms of the ground-state (GS) energy, fidelity, and the order parameter. The finite size scaling analysis for the average…

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,…

We simulate Barkhausen avalanches on fractal clusters in a two-dimensional diluted Ising ferromagnet with an effective Gaussian random field. We vary the concentration of defect sites $c$ and find a scaling region for moderate disorder,…

It is found that a large deviation function for frequency of events of size not equal to the system size in the one dimensional forest-fire model with a single ignition site at an edge is independent of the system size, by using an exact…

Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…

We analyze a recent experiment of Sharon \textit{et al.} (2003) on the coarsening, due to surface tension, of fractal viscous fingering patterns (FVFPs) grown in a radial Hele-Shaw cell. We argue that an unforced Hele-Shaw model, a natural…

We study scaling of the ground-state fidelity in neighborhoods of quantum critical points in a model of interacting spinfull fermions - a BCS-like model. Due to the exact diagonalizability of the model, in one and higher dimensions, scaling…

We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are…

The Olami--Feder--Christensen earthquake model is often considered the prototype dissipative self--organized critical model. It is shown that the size distribution of events in this model results from a complex interplay of several…