Related papers: Block scaling in the directed percolation universa…
How and why stock prices move is a centuries-old question still not answered conclusively. More recently, attention shifted to higher frequencies, where trades are processed piecewise across different timescales. Here we reveal that price…
For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our…
Monte-Carlo simulations on a variety of 2d percolating systems at criticality suggest that the excess number of clusters in finite systems over the bulk value of nc is a universal quantity, dependent upon the system shape but independent of…
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.…
We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical…
We study non-uniform percolation in a two-dimensional cluster growth model with multiple seeds. With increasing concentration of seeds, the percolation threshold is found to increase monotonically, while the exponents for correlation…
Evidence of critical dynamics has been recently found in both experiments and models of large scale brain dynamics. The understanding of the nature and features of such critical regime is hampered by the relatively small size of the…
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…
Disordered viscoelastic materials are ubiquitous and exhibit fascinating invariant scaling properties. In a companion article, we have presented comprehensive new results for the critical behavior of the dynamic susceptibility of disordered…
The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered…
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,…
A finite size scaling theory, originally developed only for transitions to absorbing states [Phys. Rev. E {\bf 92}, 062126 (2015)], is extended to distinct sorts of discontinuous nonequilibrium phase transitions. Expressions for quantities…
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…
We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…
We establish new scaling properties for the universality class of Model C, which describes relaxational critical dynamics of a nonconserved order parameter coupled to a conserved scalar density. We find an anomalous diffusion phase, which…
In this paper, we study the critical behavior of percolation on a configuration model with degree distribution satisfying an infinite second-moment condition, which includes power-law degrees with exponent $\tau \in (2,3)$. It is well known…
The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. For most concentrations of the scatterers the trajectories close…
Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction…
For systems with infinite-order phase transitions, in which an order parameter smoothly becomes nonzero, a new observable for finite-size scaling analysis is suggested. By construction this new observable has the favourable property of…