Related papers: On Coupled Directed Percolation Processes: A Unify…
The continuum percolation for Markov (or Gibbs) germ-grain models is investigated. The grains are assumed circular with random radii on a compact support. The morphological interaction is the so-called Quermass interaction defined by a…
For thermoelectric, galvanomagnetic and some other effects there may simultaneously exist two percolation thresholds, close to which the effective kinetic coefficients of macroscopically disordered media are critically dependent on the…
We study directed percolation at the upper critical transverse dimension $d=4$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) behavior. Viewing directed percolation as a kinetic process, we address…
We develop a general universality technique for establishing metric scaling limits of critical random discrete structures exhibiting mean-field behavior that requires four ingredients: (i) from the barely subcritical regime to the critical…
The q-model is a random walk model used to describe the flow of stress in a stationary granular medium. Here we derive the exact horizontal and vertical correlation functions for the q-model in two dimensions. We show that close to a…
The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we…
The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method. In case of models exhibiting Z_2 symmetric…
We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are…
It is well established that the phase transition between survival and extinction in spreading models with short-range interactions is generically associated with the directed percolation (DP) universality class. In many realistic spreading…
We study the interface representation of the contact process (CP) at its directed-percolation critical point, where the scaling properties of the interface can be related to those of the original particle model. Interestingly, such a…
We introduce a model for directed percolation with a long-range temporal diffusion, while the spatial diffusion is kept short ranged. In an interpretation of directed percolation as an epidemic process, this non-Markovian modification can…
The model of a one-dimensional kinetic contact process with parallel update is studied by the Monte Carlo simulations and finite-size scaling. The goal was to reveal the structure of the hidden percolative patterns (order parameters) in the…
Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary…
The critical exponents for a class of one-dimensional models of interface depinning in disordered media can be calculated through a mapping onto directed percolation (DP). In higher dimensions these models give rise to directed surfaces,…
We investigate the one-dimensional pair contact process with diffusion (PCPD) by extensive Monte Carlo simulations, mainly focusing on the critical density decay exponent $\delta$. To obtain an accurate estimate of $\delta$, we first find…
The dynamical relaxation and scaling properties of three different variants of the contact process in two spatial dimensions are analysed. Dynamical contact processes capture a variety of contagious processes such as the spreading of…
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…
We examine the effects of introducing a wall or edge into a directed percolation process. Scaling ansatzes are presented for the density and survival probability of a cluster in these geometries, and we make the connection to surface…
The well-established universality classes of absorbing critical phenomena are directed percolation (DP) and directed Ising (DI) classes. Recently, the pair contact process with diffusion (PCPD) has been investigated extensively and claimed…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…