Related papers: Equation of state for directed percolation
The probability distributions of the order parameter for two models in the directed percolation universality class were evaluated. Monte Carlo simulations have been performed for the one-dimensional generalized contact process and the…
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…
We study a general class of parabolic equations $$ u_t-|Du|^\gamma\big(\Delta u+(p-2) \Delta_\infty^N u\big)=0, $$ which can be highly degenerate or singular. This class contains as special cases the standard parabolic $p$-Laplace equation…
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.…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
Nonequilibrium equations of state can provide an effective thermodynamic-like description of far-from-equilibrium systems. We experimentally construct such an equation for a direct energy cascade in a turbulent two-dimensional Bose gas. Our…
The field theoretic renormalization group is applied to the stochastic Navier-Stokes equation with the stirring force correlator of the form k^(4-d-2\epsilon) in the d-dimensional space, in connection with the problem of construction of the…
We consider directed percolation processes for particle types A and B coupled unidirectionally by a transmutation reaction A -> B. It is shown that the strong coupling regime of this recently introduced problem defines a universality class…
We consider the scaling limit of the two-dimensional $q$-state Potts model for $q\leq 4$. We use the exact scattering theory proposed by Chim and Zamolodchikov to determine the one and two-kink form factors of the energy, order and disorder…
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 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…
We obtain some "universal" estimates for $L_2$-norm of the solution of a parabolic equation via a weighted version of $H^{-1}$-norm of the free term. More precisely, we found the limit upper estimate that can be achieved by transformation…
We determine the first through fourth moments of the order parameter, and various ratios, for several one- and two-dimensional models with absorbing-state phase transitions. We perform a detailed analysis of the system-size dependence of…
By employing the methods of renormalized field theory we show that the percolation behavior of random resistor-diode networks near the multicritical line belongs to the universality class of isotropic percolation. We construct a mesoscopic…
A proper formulation in the perturbative renormalization group method is presented to deduce amplitude equations. The formulation makes it possible not only avoiding a serious difficulty in the previous reduction to amplitude equations by…
We investigate the one-dimensional polaron problem and calculate the ground state energy and the effective mass. We use a real-time renormalization group method and compare our results with first and second order perturbation theory, with…
Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…
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 present a functional renormalization group approach for the active to inactive phase transition in directed percolation type systems, in which the transition is approached from the active, finite density phase. By expanding the effective…
Hard sphere systems in two dimensions are examined for arbitrary density. Simulation results are compared to the theoretical predictions for both the low and the high density limit, where the system is either disordered or ordered,…