Nóra Menyhárd

One-dimensional non-equilibrium kinetic ising models with branching annihilating random walk

Non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest-neighbour spin exchanges at T= infinity are investigated numerically from the point of view of a phase transition. The branching annihilating random walk of the ferromagnetic domain boundaries determines the steady state of the system for a range of parameters of the model. Critical exponents obtained by simulation are found to agree, within error, with those in Grassbergers cellular automata.

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 a 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 characterizing 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. The effect of an external magnetic field, leading to directed percolation-type behaviour on the level of kinks is also studied, mainly via the generalized mean-field approximation.

Hard core particle exclusion effects in low dimensional non-equilibrium phase transitions

We review the currently known universality classes of continuous phase transitions to absorbing states in non-equilibrium systems and present results of simulations and arguments to show how the blockades introduced by different particle species in one dimension cause new robust classes. Results of investigations on the dynamic scaling behavior of some bosonic spreading models are reported.

Critical behavior of an even-offspringed branching and annihilating random-walk cellular automaton with spatial disorder

A stochastic cellular automaton exhibiting a parity-conserving class transition has been investigated in the presence of quenched spatial disorder by large-scale simulations. Numerical evidence has been found that weak disorder causes irrelevant perturbation for the universal behavior of the transition and the absorbing phase of this model. This opens up the possibility for experimental observation of the critical behavior of a nonequilibrium phase transition to absorbing state. For very strong disorder the model breaks up into blocks with exponential-size distribution and continuously changing critical exponents are observed. For strong disorder the randomly distributed diffusion walls introduce another transition within the inactive phase of the model, in which residual particles survive the extinction. The critical dynamical behavior of this transition has been explored.

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

The A+A-->0, B+B-->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 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 the standard annihilating random walk of two species. Time dependent simulations are presented here to illustrate differences caused by exclusion in scaling properties of the 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 and lead to deviations from standard annihilating random walk behavior.

Non-Markovian persistence at the parity conserving point of a one-dimensional nonequilibrium kinetic Ising model

One-dimensional nonequilibrium 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 and the exponent characterizing the two-time autocorrelation function of the total magnetization under nonequilibrium conditions are reported. It is found that the critical fluctuations at the PC transition have a strong effect on the spins: the behaviour becomes non-Markovian and the above exponents exhibit drastic changes as compared with the Markovian Glauber - Ising case. In this context the crucial importance of considering the global order parameter (instead of the local one) is emphasized.

Nonequilibrium kinetic Ising models: phase transitions and universality classes in one dimension

Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and Kawasaki-type spin-exchange kinetics at infinite temperature T are investigated here in one dimension from the point of view of phase transition and critical behaviour. Branching annihilating random walks with an even number of offspring (on the part of the ferromagnetic domain boundaries), is a decisive process in forming the steady state of the system for a range of parameters, in the family of models considered. A wide variety of quantities characterize the critical behaviour of the system. Results of computer simulations and of a generalized mean field theory are presented and discussed.

Multispecies 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 multispecies annihilating random walk transition found at zero branching rate previously is investigated now concerning the cluster behavior 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.

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 characterizing spin-cluster growth. We have investigated here numerically these exponents in the non-equilibrium generalization 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.

One-dimensional nonequilibrium kinetic Ising models with local spin symmetry breaking: N-component branching annihilating random-walk 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.