Related papers: Field-theoretic analysis of directed percolation: …
In this work, we employ a field-theoretic renormalization group approach to study a paradigmatic model of directed percolation. We focus on the perturbative calculation of the equation of state, extending the analysis to the three-loop…
The general epidemic process is a paradigmatic model in non-equilibrium statistical physics displaying a continuous phase transition between active and absorbing states.The dynamic isotropic percolation universality class captures its…
A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened…
The paradigmatic model of the directed percolation process is studied near its second order phase transition between an absorbing and an active state. The model is first expressed in a form of Langevin equation and later rewritten into a…
Using perturbative renormalization group we study the influence of random velocity field on the critical behaviour of directed bond percolation process near its second-order phase transition between absorbing and active phase. We consider…
The directed percolation process in the vicinity of non-equilibrium phase transition is studied by the means of field theoretic methods. It will be assumed that percolation takes place in a compressible environment, which will be generated…
This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The…
We formulate directed percolation in (1+1) dimensions in the language of a reaction-diffusion process with exclusion taking place in one space dimension. We map the master equation that describes the dynamics of the system onto a quantum…
Using perturbative renormalization group we investigate the influence of random velocity field on the critical behavior of directed bond percolation process near its second-order phase transition between absorbing and active phase.…
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 review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous non-equilibrium active to absorbing state phase transitions whose asymptotic…
The directed bond percolation process is studied in the presence of com- pressible velocity fluctuations with long-range correlations. We discuss a construction of a field theoretic action and a way of obtaining its large scale properties…
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…
Using field-theoretic renormalization group methods we calculate the equation of state for non-equilibrium systems belonging to the universality class of directed percolation (Gribov process) to second order in epsilon = 4-d. By introducing…
We investigate non-equilibrium critical phenomena using a nonperturbative renormalization group method. Reaction-diffusion processes are described by a scale dependent effective action which evolution is governed by very generic flow…
Universal behavior is a typical emergent feature of critical systems. A paramount model of the non-equilibrium critical behavior is the directed bond percolation process that exhibits an active- to-absorbing state phase transition in the…
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…