arXiv subjects

Geza Odor

Publications and source records attributed to Geza Odor.

At least 37 records · Page 2Linked to original sources

arXiv2003

Phase transition classes in triplet and quadruplet reaction diffusion models

Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n=3,4 parents, whereas explicit diffusion of single particles (A) is present are investigated in low dimensions by mean-field approximation and simulations. The mean-field approximation of general nA -> (n+k)A, mA -> (m-l)A type of lattice models is solved and novel kind of critical behavior is pointed out. In d=2 dimensions the 3A -> 4A, 3A -> 2A model exhibits a continuous mean-field type of phase transition, that implies d_c<2 upper critical dimension. For this model in d=1 extensive simulations support a mean-field type of phase transition with logarithmic corrections unlike the Park et al.'s recent study (Phys. Rev E {\bf 66}, 025101 (2002)). On the other hand the 4A -> 5A, 4A -> 3A quadruplet model exhibits a mean-field type of phase transition with logarithmic corrections in d=2, while quadruplet models in 1d show robust, non-trivial transitions suggesting d_c=2. Furthermore I show that a parity conserving model 3A -> 5A, 2A->0 in d=1 has a continuous phase transition with novel kind of exponents. These results are in contradiction with the recently suggested implications of a phenomenological, multiplicative noise Langevin equation approach and with the simulations on suppressed bosonic systems by Kockelkoren and Chaté (cond-mat/0208497).

cond-mat.stat-mech↗

arXiv2003

Critical behavior in reaction-diffusion systems exhibiting absorbing phase transition

Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field approximation and simulations are given which support novel kind of non-equilibrium criticality. These are in contradiction with the implications of a suggested phenomenological, multiplicative noise Langevin equation approach and with some of recent numerical analysis. Simulation results for the one and two dimensional binary spreading 2A -> 4A, 4A -> 2A model display a new type of mean-field criticality characterized by alpha=1/3 and beta=1/2 critical exponents suggested in cond-mat/0210615.

cond-mat.stat-mech↗

arXiv2002

On the critical behavior of the one dimensional, diffusive pair contact process

The phase transition of the one-dimensional, diffusive pair contact process (PCPD) is investigated by N cluster mean-field approximations and high precision simulations. The N=3,4 cluster approximations exhibit smooth transition line to absorbing state by varying the diffusion rate D with beta_2=2 mean-field order parameter exponent of the pair density. This contradicts with former N=2 results, where two different mean-field behavior was found along the transition line. Extensive dynamical simulations on L=10^5 lattices give estimates for the order parameter exponents of the particles for 0.05 <= D <= 0.7. These data can support former two distinct class findings. However the gap between low and high D exponents is narrower than estimated previously and the possibility for interpreting numerical data as a single class behavior with exponents alpha=0.21(1), beta=0.41(1) assuming logarithmic corrections is shown. Finite size scaling and cluster simulation results are also presented.

cond-mat.stat-mech↗

arXiv2002

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 nonequilibrium 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.

cond-mat.stat-mech↗

arXiv2001

Multicomponent binary spreading process

I investigate numerically the phase transitions of two-component generalizations of binary spreading processes in one dimension. In these models pair annihilation: AA->0, BB->0, explicit particle diffusion and binary pair production processes compete with each other. Several versions with spatially different productions have been explored and shown that for the cases: 2A->3A, 2B->3B and 2A->2AB, 2B->2BA a phase transition occurs at zero production rate ($σ=0$), that belongs to the class of N-component, asymmetric branching and annihilating random walks, characterized by the order parameter exponent $β=2$. In the model with particle production: AB->ABA, BA-> BAB a phase transition point can be located at $σ_c=0.3253$ that belongs to the class of the one-component binary spreading processes.

cond-mat.stat-mech↗

arXiv2001

Pair contact process with a particle source

We study the phase diagram and critical behavior of the one-dimensional pair contact process (PCP) with a particle source using cluster approximations and extensive simulations. The source creates isolated particles only, not pairs, and so couples not to the order parameter (the pair density) but to a non-ordering field, whose state influences the evolution of the order parameter. While the critical point p_c shows a singular dependence on the source intensity, the critical exponents appear to be unaffected by the presence of the source, except possibly for a small change in beta. In the course of our study we obtain high-precision values for the critical exponents of the standard PCP, confirming directed-percolation-like scaling.

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arXiv2001

On the critical behavior of a lattice prey-predator model

The critical properties of a simple prey-predator model are revisited. For some values of the control parameters, the model exhibits a line of directed percolation like transitions to a single absorbing state. For other values of the control parameters one finds a second line of continuous transitions toward infinite number of absorbing states, and the corresponding steady-state exponents are mean-field like. The critical behavior of the special point T (bicritical point), where the two transition lines meet, belongs to a different universality class. The use of dynamical Monte-Carlo method shows that a particular strategy for preparing the initial state should be devised to correctly describe the physics of the system near the second transition line. Relationships with a forest fire model with immunization are also discussed.

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arXiv2001

Critical branching-annihilating random walk of two species

The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk with two offsprings. It is shown that two-dimensional simulations confirm the field theoretical results with logarithmic corrections. In one dimension, however, if particles exhibit hard core interaction I confirm the very recent predictions of Kwon et al. [PRL {\bf 85}, 1682 (2000)] that there are two different universality classes depending on the spatial symmetry of the offspring production characterized by $β_S=0.5$ and $β_A=2$. Elaborate analysis of simulation data shows that the order parameter exponent $β$ does not depend on initial conditions or on diffusion rates of species but strong correction to scaling is observed. By systematic numerical simulations the critical point properties have been explored and initial condition dependence of the dynamical exponents $Z$ and $α$ is shown. In the case of a random initial state the particle-density decay at the critical point follows the $t^{-1/4}$ law with logarithmic corrections.

cond-mat.stat-mech↗

arXiv2000

Phase transition of the one-dimensional coagulation-production process

Recently an exact solution has been found (M.Henkel and H.Hinrichsen, cond-mat/0010062) for the 1d coagulation production process: 2A ->A, A0A->3A with equal diffusion and coagulation rates. This model evolves into the inactive phase independently of the production rate with $t^{-1/2}$ density decay law. Here I show that cluster mean-field approximations and Monte Carlo simulations predict a continuous phase transition for higher diffusion/coagulation rates as considered in cond-mat/0010062. Numerical evidence is given that the phase transition universality agrees with that of the annihilation-fission model with low diffusions.

cond-mat.stat-mech↗

arXiv2000

The universal behavior of one-dimensional, multi-species branching and annihilating random walks with exclusion

A directed percolation process with two symmetric particle species exhibiting exclusion in one dimension is investigated numerically. It is shown that if the species are coupled by branching ($A\to AB$, $B\to BA$) a continuous phase transition will appear at zero branching rate limit belonging to the same universality class as that of the dynamical two-offspring (2-BARW2) model. This class persists even if the branching is biased towards one of the species. If the two systems are not coupled by branching but hard-core interaction is allowed only the transition will occur at finite branching rate belonging to the usual 1+1 dimensional directed percolation class.

cond-mat.stat-mech↗

arXiv2000

Critical behaviour of the 1d annihilation fission process 2A->0, 2A->3A

Numerical simulations and cluster mean-field approximations with coherent anomaly extrapolation show that the critical line of the 1d annihilation fission process is separated into two regions. In both the small and high diffusion cases the critical behavior is different from the well known universality classes of non-equilibrium phase transitions to absorbing states. The high diffusion region seems to be well described by the cyclically coupled directed percolation and annihilating random walk. Spreading exponents show non-universal behavior.

cond-mat.stat-mech↗

arXiv2000

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.

cond-mat.stat-mech↗

arXiv2000

Nonequilibrium Kinetic Ising Models: Phase Transition 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.

cond-mat.stat-mech↗

arXiv1999

Critical behavior of roughening transitions in parity-conserving growth processes

We investigate a class of parity-conserving solid-on-solid models which describe the growth of an interface by the deposition and evaporation of dimers. As a key feature of the models, evaporation of dimers takes place only at the edges of terraces, leading to a roughening transition between a smooth and a rough phase. We consider several variants of growth models in order to identify universal and nonuniversal properties. Moreover, a parity-conserving polynuclear growth model is proposed. All variants display the same type of universal critical behavior at the roughening transition. Because of parity-conservation, the critical behavior at the first few layers can be explained in terms of unidirectionally coupled branching annihilating random walks with even number of offspring.

cond-mat.stat-mech↗

arXiv1998

Roughening transition in a model for dimer adsorption and desorption

A solid-on-solid growth model for dimer adsorption and desorption is introduced and studied numerically. The special property of the model is that dimers can only desorb at the edges of terraces. It is shown that the model exhibits a roughening transition from a smooth to a rough phase. In both phases the interface remains pinned to the bottom layer and does not propagate. Close to the transition certain critical properties are related to those of a unidirectionally coupled hierarchy of parity-conserving branching-annihilating random walks.

cond-mat.stat-mech↗

arXiv1998

The relaxation of initial condition in systems with infinitely many absorbing states

We have investigated the effect of the initial condition on the spreading exponents of the one-dimensional pair contact process (PCP) and threshold transfer process (TTP).The non-order field was found to exhibit critical fluctuations, relaxing to its natural value with the same power-law as the order parameter field. We argue that this slow relaxation, which was not taken into account in earlier studies of these models, is responsible for the continuously changing survival probability exponent. High precision numerical simulations show evidence of a(slight) dependence of the location of the transition point on the initial concentration, in the case of PCP. The damage spreading (DS) point and the spreading exponents coincide with those of the ordinary critical point in both cases.

cond-mat.stat-mech↗

arXiv1998

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.

cond-mat.stat-mech↗

arXiv1998

Correlated Initial Conditions in Directed Percolation

We investigate the influence of correlated initial conditions on the temporal evolution of a (d+1)-dimensional critical directed percolation process. Generating initial states with correlations ~r^(sigma-d) we observe that the density of active sites in Monte-Carlo simulations evolves as rho(t)~t^kappa. The exponent kappa depends continuously on sigma and varies in the range -beta/nu_{||}<=kappa<=eta. Our numerical results are confirmed by an exact field-theoretical renormalization group calculation.

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