Compact parity conserving percolation in one-dimension

Compact directed percolation is known to appear at the endpoint of the directed percolation critical line of the Domany-Kinzel cellular automaton in 1+1 dimension. Equivalently, such transition occurs at zero temperature in a magnetic field H, upon changing the sign of H, in the one-dimensional Glauber-Ising model with well known exponents characterising spin-cluster growth. We have investigated here numerically these exponents in the non-equilibrium generalization (NEKIM) of the Glauber model in the vicinity of the parity-conserving phase transition point of the kinks. Critical fluctuations on the level of kinks are found to affect drastically the characteristic exponents of spreading of spins while the hyperscaling relation holds in its form appropriate for compact clusters.Comment: 7 pages, 7 figures embedded in the latex, final form before J.Phys.A publicatio

Szakmai tevékenység az MNTA TTK Polimer Fizikai Kutatócsoportjában és a BME Műanyag és Gumiipari Laboratóriumában

A Muanyag- és Gumiipari Laboratórium aktívan részt vesz a Budapesti Muszaki és Gazdaságtudományi Egyetem vegyészmérnök és biomérnök képzésében, valamint az országban egyedülálló módon elindítottuk az önálló Muanyag- és Száltechnológiai Mesterszak-ot. Az oktatás mellett, kutatócsoportunk a polimerek feldolgozásához és alkalmazási területeihez kapcsolódóan végez szerteágazó kutatómunkát

Non-Markovian Persistence at the PC point of a 1d non-equilibrium kinetic Ising model

One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are investigated here numerically from the point of view of the underlying spin system. The dynamical persistency exponent $\Theta$ and the exponent $lambda$ characterising the two-time autocorrelation function of the total magnetization under non-equilibrium conditions are reported. It is found that the PC transition has strong effect: the process becomes non-Markovian and the above exponents exhibit drastic changes as compared to the Glauber-Ising case.Comment: 6 pages, Latex, postscript figures include

Crossovers from parity conserving to directed percolation universality

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 absorbing phases (the NEKIMCA and Grassberger's A stochastic cellular automaton) the introduction of an external symmetry breaking field causes a crossover to kink parity conserving models characterized by dynamical scaling of the directed percolation (DP) and the crossover exponent: 1/\phi ~ 0.53(2). In case an even offspringed branching and annihilating random walk model (dual to NEKIMCA) the introduction of spontaneous particle decay destroys the parity conservation and results in a crossover to the DP class characterized by the crossover exponent: 1/\phi\simeq 0.205(5). The two different kinds of crossover operators can't be mapped onto each other and the resulting models show a diversity within the DP universality class in one dimension. These 'sub-classes' differ in cluster scaling exponents.Comment: 6 pages, 6 figures, accepted version in PR

One-dimensional spin-anisotropic kinetic Ising model subject to quenched disorder

Large-scale Monte Carlo simulations are used to explore the effect of quenched disorder on one dimensional, non-equilibrium kinetic Ising models with locally broken spin symmetry, at zero temperature (the symmetry is broken through spin-flip rates that differ for '+' and '-' spins). The model is found to exhibit a continuous phase transition to an absorbing state. The associated critical behavior is studied at zero branching rate of kinks, through analysis spreading of '+' and '-' spins and, of the kink density. Impurities exert a strong effect on the critical behavior only for a particular choice of parameters, corresponding to the strongly spin-anisotropic kinetic Ising model introduced by Majumdar et al. Typically, disorder effects become evident for impurity strengths such that diffusion is nearly blocked. In this regime, the critical behavior is similar to that arising, for example, in the one-dimensional diluted contact process, with Griffiths-like behavior for the kink density. We find variable cluster exponents, which obey a hyperscaling relation, and are similar to those reported by Cafiero et al. We also show that the isotropic two-component AB -> 0 model is insensitive to reaction-disorder, and that only logarithmic corrections arise, induced by strong disorder in the diffusion rate.Comment: 10 pages, 13 figures. Final, accepted form in PRE, including a new table summarizing the molde

Study of the multi-species annihilating random walk transition at zero branching rate - cluster scaling behavior in a spin model

Numerical and theoretical studies of a one-dimensional spin model with locally broken spin symmetry are presented. The multi-species annihilating random walk transition found at zero branching rate previously is investigated now concerning the cluster behaviour of the underlying spins. Generic power law behaviors are found, besides the phase transition point, also in the active phase with fulfillment of the hyperscaling law. On the other hand scaling laws connecting bulk- and cluster exponents are broken - a possibility in no contradiction with basic scaling assumptions because of the missing absorbing phase.Comment: 7 pages, 6 figures, final form to appear in PRE Nov.200

Phase transitions and critical behaviour in one-dimensional non-equilibrium kinetic Ising models with branching annihilating random walk of kinks

One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest-neighbour spin exchanges exhibiting directed percolation-like parity conserving(PC) phase transition on the level of kinks are now further investigated, numerically, from the point of view of the underlying spin system. Critical exponents characterising its statics and dynamics are reported. It is found that the influence of the PC transition on the critical exponents of the spins is strong and the origin of drastic changes as compared to the Glauber-Ising case can be traced back to the hyperscaling law stemming from directed percolation(DP). Effect of an external magnetic field, leading to DP-type critical behaviour on the level of kinks, is also studied, mainly through the generalised mean field approximation.Comment: 15 pages, using RevTeX, 13 Postscript figures included, submitted to J.Phys.A, figures 12 and 13 fixe

One-dimensional Nonequilibrium Kinetic Ising Models with local spin-symmetry breaking: N-component branching annihilation transition at zero branching rate

The effects of locally broken spin symmetry are investigated in one dimensional nonequilibrium kinetic Ising systems via computer simulations and cluster mean field calculations. Besides a line of directed percolation transitions, a line of transitions belonging to N-component, two-offspring branching annihilating random-walk class (N-BARW2) is revealed in the phase diagram at zero branching rate. In this way a spin model for N-BARW2 transitions is proposed for the first time.Comment: 6 pages, 5 figures included, 2 new tables added, to appear in PR

Critical behaviour of annihilating random walk of two species with exclusion in one dimension

The $A+A\to 0$, $B+B\to 0$ process with exclusion between the different kinds is investigated here numerically. Before treating this model explicitly, we study the generalized Domany-Kinzel cellular automaton model of Hinrichsen on the line of the parameter space where only compact clusters can grow. The simplest version is treated with two absorbing phases in addition to the active one. The two kinds of kinks which arise in this case do not react, leading to kinetics differing from standard annihilating random walk of two species. Time dependent simulations are presented here to illustrate the differences caused by exclusion in the scaling properties of usually discussed characteristic quantities. The dependence on the density and composition of the initial state is most apparent. Making use of the parallelism between this process and directed percolation limited by a reflecting parabolic surface we argue that the two kinds of kinks exert marginal perturbation on each other leading to deviations from standard annihilating random walk behavior.Comment: 12 pages, 16 figures, small typos corrected, 2 references adde