Related papers: Universal Scaling of Gap Dynamics in Percolation

Critical quantum metrology aims to harness critical properties near quantum phase transitions to enhance parameter estimation precision. However, critical slowing down inherently limits the achievable precision within a finite evolution…

Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the…

We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…

Explosive percolation in the Achlioptas process, which has attracted much research attention, is known to exhibit a rich variety of critical phenomena that are anomalous from the perspective of continuous phase transitions. Hereby, we show…

We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…

We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition…

It is shown that the universal critical properties of two recently introduced coupled directed percolation processes can be described by a single rapidity reversal invariant stochastic reaction-diffusion model. It is demonstrated that all…

We discuss the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group…

Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…

We consider the influence of a power-law deviation from the critical coupling such that the system is critical at its surface. We develop a scaling theory showing that such a perturbation introduces a new length scale which governs the…

Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…

Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…

The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…

Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…

We present the results of computer simulations on a class of percolative systems that forms a new universality class. We show the results for the critical exponents for this new class, inferred from simulations of two- and three-dimensional…

The macroscopic fluctuation theory provides a complete hydrodynamic description of non-equilibrium classical diffusive systems. As a first step towards a diffusive theory of open quantum systems, we show how to construct a microscopic open…

We study the scaling properties of critical particle systems confined by a potential. Using renormalization-group arguments, we show that their critical behavior can be cast in the form of a trap-size scaling, resembling finite-size scaling…

Using grand canonical Monte Carlo simulations, we investigate the percolation behavior of a square well fluid with an ultra-short range of attraction in three dimension (3D) and in confined geometry. The latter is defined through two…

In this paper the percolation of monomers on a square lattice is studied as the particles interact with either repulsive or attractive energies. By means of a finite-size scaling analysis, the critical exponents and the scaling collapsing…

Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms and urban growth is one of the most eminent transformative processes. We analyze global land cover…