Related papers: Critical exponents of the explosive percolation tr…
One possible framework to interpret the irreversibility transition observed in periodically driven colloidal suspensions is that of a non-equilibrium phase transition towards an absorbing reversible state at low amplitude of the driving…
The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…
Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…
In this work we consider the two-dimensional percolation model arising from the majority dynamics process at a given time $t\in\mathbb{R}_+$. We show the emergence of a sharp threshold phenomenon for the box crossing event at the critical…
We show that an out-of-equilibrium percolation transition occurs after quenching ferromagnetic Ising-like systems across their magnetic first-order transitions. As a paradigmatic example, we consider a two-dimensional Ising system driven…
Clusters generated by the product-rule growth model of Achlioptas, D'Souza, and Spencer on a two-dimensional square lattice are shown to obey qualitatively different scaling behavior than standard (random growth) percolation. The threshold…
Through studying the critical phenomena in continuum-percolation of discs, we find a new approach to locate the critical point, i.e. using the inflection point of $P_\infty$ as an evaluation of the percolation threshold. The susceptibility,…
The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition,…
The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…
In this work, we revisited the Ziff-Gulari-Barshad (ZGB) model to study its phase transitions and critical exponents through time-dependent Monte Carlo simulations. We used a method proposed recently to locate the non-equilibrium…
We study the critical behavior for percolation on inhomogeneous random networks on $n$ vertices, where the weights of the vertices follow a power-law distribution with exponent $\tau \in (2,3)$. Such networks, often referred to as…
We consider first-passage percolation on $\mathbb{Z}^2$ with i.i.d. weights, whose distribution function satisfies $F(0) = p_c = 1/2$. This is sometimes known as the "critical case" because large clusters of zero-weight edges force passage…
Bootstrap percolation on a graph iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product measure, and we say that spanning…
Motivated by an application in wireless telecommunication networks, we consider a two-type continuum-percolation problem involving a homogeneous Poisson point process of users and a stationary and ergodic point process of base stations.…
Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a pre-critical to the…
As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two $k$-cliques means that they share at least $l<k$ vertices. In this paper, we develop a theoretical…
We perform large-scale numerical simulations to investigate the critical behavior of $k$-core percolation in two dimensions with an extended interaction range $r$. By systematically varying both the core index $k$ and the interaction range…
Directed percolation(DP) has recently emerged as a possible solution to the century old puzzle surrounding the transition to turbulence. Multiple model studies reported DP exponents, however experimental evidence is limited since the…
Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the…