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We numerically investigate the approach to the stationary state in the nonconservative Olami-Feder-Christensen (OFC) model for earthquakes. Starting from initially random configurations, we monitor the average earthquake size in different…
Dissipative phase transitions are strongly shaped by the symmetries of the Liouvillian, yet the quantitative impact of weak and strong symmetries on critical behavior has remained unclear. We study a squeezed-photon model with single- and…
We consider quantum walks defined on arbitrary infinite graphs, parameterized by a family of scattering matrices attached to the vertices. Multiplying each scattering matrix by an i.i.d. random phase, we obtain a random scattering quantum…
Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for…
In this chapter of the e-book "Self-Organized Criticality Systems" we summarize some theoretical approaches to self-organized criticality (SOC) phenomena that involve percolation as an essential key ingredient. Scaling arguments, random…
With Monte Carlo methods, we simulate the critical domain-wall dynamics of model B, taking the two-dimensional Ising model as an example. In the macroscopic short-time regime, a dynamic scaling form is revealed. Due to the existence of the…
We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…
Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…
The $q$-model, a random walk model rich in behaviour and applications, is investigated. We introduce and motivate the $q$-model via its application proposed by Coppersmith {\em et al.} to the flow of stress through granular matter at rest.…
Recently, Takayasu and Tretyakov [Phys. Rev. Lett. {\bf 68}, 3060 (1992)], studied branching annihilating random walks (BAW) with $n=1$-5 offspring. These models exhibit a continuous phase transition to an absorbing state. For odd $n$ the…
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time…
The critical behaviour of directed self-avoiding walks is studied on parabolic-like systems with a free boundary at x=\pm Ct^\alpha. Using a scaling argument, 1/C is shown to be a marginal variable when \alpha=\nu_\perp/\nu_\parallel=1/2,…
The critical properties of short-range Ising spin-glass models, defined on a diamond hierarchical lattice of graph fractal dimension $d_{f}=2.58$, 3, and 4, and scaling factor 2 are studied via a method based on the Migdal-Kadanoff…
The critical dynamics of Ising spin glasses with Bimodal, Gaussian, and Laplacian interaction distributions are studied numerically in dimensions 3 and 4. The data demonstrate that in both dimensions the critical dynamic exponent $z_{\rm…
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…
Activated Random Walk is a particle system displaying Self-Organized Criticality, in that the dynamics spontaneously drive the system to a critical state. How universal is this critical state? We state many interlocking conjectures aimed at…
Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations $p=0.95$ and 0.8 at criticality. In contrast to studies of the critical behavior of the…
We make an extensive numerical study of a two dimensional nonconservative model proposed by Olami-Feder-Christensen to describe earthquake behavior. By analyzing the distribution of earthquake sizes using a multiscaling method, we find…
We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum…
We introduce two coupled map lattice models with nonconservative interactions and a continuous nonlinear driving. Depending on both the degree of conservation and the convexity of the driving we find different behaviors, ranging from…