Related papers: Explosive Percolation: Unusual Transitions of a Si…
We simulate the two-dimensional XY model in the flow representation by a worm-type algorithm, up to linear system size $L=4096$, and study the geometric properties of the flow configurations. As the coupling strength $K$ increases, we…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
We study critical spreading in a surface-modified directed percolation model in which the left- and right-most sites have different occupation probabilities than in the bulk. As we vary the probability for growth at an edge, the critical…
The use of machine learning techniques in classical and quantum systems has led to novel techniques to classify ordered and disordered phases, as well as uncover transition points in critical phenomena. Efforts to extend these methods to…
A random growth lattice filling model of percolation with touch and stop growth rule is developed and studied numerically on a two dimensional square lattice. Nucleation centers are continuously added one at a time to the empty sites and…
We propose a statistical model defined on the three-dimensional diamond network where the splitting of randomly selected nodes leads to a spatially disordered network, with decreasing degree of connectivity. The terminal state, that is…
The renowned general epidemic process describes the stochastic evolution of a population of individuals which are either susceptible, infected or dead. A second order phase transition belonging to the universality class of dynamic isotropic…
Percolation theory has been widely used to study phase transitions in complex networked systems. It has also successfully explained several macroscopic phenomena across different fields. Yet, the existent theoretical framework for…
This is a comprehensive report on the phase transition between two turbulent states of electroconvection in nematic liquid crystals, which was recently found by the authors to be in the directed percolation (DP) universality class [K. A.…
Directed percolation is one of the most prominent universality classes of nonequilibrium phase transitions and can be found in a large variety of models. Despite its theoretical success, no experiment is known which clearly reproduces the…
We study a two-dimensional kinetic Ising model with Swendsen-Wang dynamics, replacing the usual percolation on top of Ising clusters by explosive percolation. The model exhibits a reversible first-order phase transition with hysteresis.…
We study an explosive percolation model in which a link is randomly added and neighboring nodes sequentially rewire their links to suppress the growth of large clusters. In this manner, the rewiring nodes spread outward starting from the…
Models of one-dimensional driven diffusive systems sometimes exhibit an abrupt increase of the correlation length to an anomalously large but finite value as the parameters of the model are varied. This behavior may be misinterpreted as a…
We introduce and study a new percolation model, inspired by recent works on jigsaw percolation, graph bootstrap percolation, and percolation in polluted environments. Start with an oriented graph $G_0$ of initially occupied edges on $n$…
Let $\{\xi_i\}_{i \geq 1}$ be a sequence of i.i.d.\ positive random variables. Starting from the usual square lattice replace each horizontal edge that links a site in $i$-th vertical column to another in the $(i+1)$-th vertical column by…
The description of thermodynamic phase transitions in terms of percolation transitions of suitably defined clusters has a long tradition and boasts a number of important successes, the most prominent ones being in ferromagnetic lattice…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…
An analysis of water clustering is used to study the quasi-2D percolation transition of water adsorbed at planar hydrophilic surfaces. Above the critical temperature of the layering transition (quasi-2D liquid-vapor phase transition of…
Experimental evidence of an absorbing phase transition, so far associated with spatio-temporal dynamics is provided in a purely temporal optical system. A bistable semiconductor laser, with long-delayed opto-electronic feedback and…