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Geza Odor

Publications and source records attributed to Geza Odor.

At least 19 recordsLinked to original sources
arXiv2019

Avalanche dynamics in higher dimensional fiber bundle models

We investigate how the dimensionality of the embedding space affects the microscopic crackling dynamics and the macroscopic response of heterogeneous materials. Using a fiber bundle model with localized load sharing computer simulations are performed from 1 to 8 dimensions slowly increasing the external load up to failure. Analyzing the constitutive curve, fracture strength and avalanche statistics of bundles we demonstrate that a gradual crossover emerges from the universality class of localized behavior to the mean field class of fracture as the embedding dimension increases. The evolution between the two universality classes is described by an exponential functional form. Simulations revealed that the average temporal profile of crackling avalanches evolves with the dimensionality of the system from a strongly asymmetric shape to a symmetric parabola characteristic for localized stresses and homogeneous stress fields, respectively.

cond-mat.dis-nn↗
arXiv2012

Slow dynamics and rare-region effects in the contact process on weighted tree networks

We show that generic, slow dynamics can occur in the contact process on complex networks with a tree-like structure and a superimposed weight pattern, in the absence of additional (non-topological) sources of quenched disorder. The slow dynamics is induced by rare-region effects occurring on correlated subspaces of vertices connected by large weight edges, and manifests in the form of a smeared phase transition. We conjecture that more sophisticated network motifs could be able to induce Griffiths phases, as a consequence of purely topological disorder.

cond-mat.stat-mech↗
arXiv2010

Surface pattern formation and scaling described by conserved lattice gases

We extend our 2+1 dimensional discrete growth model (PRE 79, 021125 (2009)) with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence. By mapping the slopes onto particles two-dimensional, nonequilibrium binary lattice model emerge, in which the (smoothing/roughening) surface diffusion can be described by attracting or repelling motion of oriented dimers. The binary representation allows simulations on very large size and time scales. We provide numerical evidence for Mullins-Herring or molecular beam epitaxy class scaling of the surface width. The competition of inverse Mullins-Herring diffusion with a smoothing deposition, which corresponds to a Kardar-Parisi-Zhang (KPZ) process generates different patterns: dots or ripples. We analyze numerically the scaling and wavelength growth behavior in these models. In particular we confirm by large size simulations that the KPZ type of scaling is stable against the addition of this surface diffusion, hence this is the asymptotic behavior of the Kuramoto-Sivashinsky equation as conjectured by field theory in two dimensions, but has been debated numerically. If very strong, normal surface diffusion is added to a KPZ process we observe smooth surfaces with logarithmic growth, which can describe the mean-field behavior of the strong-coupling KPZ class. We show that ripple coarsening occurs if parallel surface currents are present, otherwise logarithmic behavior emerges.

cond-mat.stat-mech↗
arXiv2010

Directed d-mer diffusion describing Kardar-Parisi-Zhang type of surface growth

We show that d+1-dimensional surface growth models can be mapped onto driven lattice gases of d-mers. The continuous surface growth corresponds to one dimensional drift of d-mers perpendicular to the (d-1)-dimensional "plane" spanned by the d-mers. This facilitates efficient, bit-coded algorithms with generalized Kawasaki dynamics of spins. Our simulations in d=2,3,4,5 dimensions provide scaling exponent estimates on much larger system sizes and simulations times published so far, where the effective growth exponent exhibits an increase. We provide evidence for the agreement with field theoretical predictions of the Kardar-Parisi-Zhang universality class and numerical results. We show that the (2+1)-dimensional exponents conciliate with the values suggested by Lassig within error margin, for the largest system sizes studied here, but we can't support his predictions for (3+1)d numerically.

cond-mat.stat-mech↗
arXiv2009

On the absorbing-state phase transition in the one-dimensional triplet creation model

We study the lattice reaction diffusion model 3A -> 4A, A -> 0 (``triplet creation") using numerical simulations and n-site approximations. The simulation results provide evidence of a discontinuous phase transition at high diffusion rates. In this regime the order parameter appears to be a discontinuous function of the creation rate; no evidence of a stable interface between active and absorbing phases is found. Based on an effective mapping to a modified compact directed percolation process, shall nevertheless argue that the transition is continuous, despite the seemingly discontinuous phase transition suggested by studies of finite systems.

cond-mat.stat-mech↗
arXiv2009

Mapping of 2+1-dimensional Kardar-Parisi-Zhang growth onto a driven lattice gas model of dimer

We show that a 2+1 dimensional discrete surface growth model exhibiting Kardar-Parisi-Zhang (KPZ) class scaling can be mapped onto a two dimensional conserved lattice gas model of directed dimers. In case of KPZ height anisotropy the dimers follow driven diffusive motion. We confirm by numerical simulations that the scaling exponents of the dimer model are in agreement with those of the 2+1 dimensional KPZ class. This opens up the possibility of analyzing growth models via reaction-diffusion models, which allow much more efficient computer simulations.

cond-mat.stat-mech↗
arXiv2008

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/ϕ~ 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/ϕ\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.

cond-mat.stat-mech↗
arXiv2007

Self-organizing, two-temperature Ising model describing human segregation

A two-temperature Ising-Schelling model is introduced and studied for describing human segregation. The self-organized Ising model with Glauber kinetics simulated by Müller et al. exhibits a phase transition between segregated and mixed phases mimicking the change of tolerance (local temperature) of individuals. The effect of external noise is considered here as a second temperature added to the decision of individuals who consider change of accommodation. A numerical evidence is presented for a discontinuous phase transition of the magnetization.

physics.soc-ph↗
arXiv2007

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.

cond-mat.stat-mech↗
arXiv2006

The phase transition of triplet reaction-diffusion models

The phase transitions classes of reaction-diffusion systems with multi-particle reactions is an open challenging problem. Large scale simulations are applied for the 3A -> 4A, 3A -> 2A and the 3A -> 4A, 3A->0 triplet reaction models with site occupation restriction in one dimension. Static and dynamic mean-field scaling is observed with signs of logarithmic corrections suggesting d_c=1 upper critical dimension for this family of models.

cond-mat.stat-mech↗
arXiv2006

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

A stochastic cellular automaton exhibiting 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 to 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.

cond-mat.stat-mech↗
arXiv2005

Cluster mean-field study of the parity conserving phase transition

The phase transition of the even offspringed branching and annihilating random walk is studied by N-cluster mean-field approximations on one-dimensional lattices. By allowing to reach zero branching rate a phase transition can be seen for any N <= 12.The coherent anomaly extrapolations applied for the series of approximations results in $ν_{\perp}=1.85(3)$ and $β=0.96(2)$.

cond-mat.stat-mech↗
arXiv2004

The role of diffusion in branching and annihilation random walk models

Different branching and annihilating random walk models are investigated by cluster mean-field method and simulations in one and two dimensions. In case of the A -> 2A, 2A -> 0 model the cluster mean-field approximations show diffusion dependence in the phase diagram as was found recently by non-perturbative renormalization group method (L. Canet et al., cond-mat/0403423). The same type of survey for the A -> 2A, 4A -> 0 model results in a reentrant phase diagram, similar to that of 2A -> 3A, 4A -> 0 model (G. Ódor, PRE {\bf 69}, 036112 (2004)). Simulations of the A -> 2A, 4A -> 0 model in one and two dimensions confirm the presence of both the directed percolation transitions at finite branching rates and the mean-field transition at zero branching rate. In two dimensions the directed percolation transition disappears for strong diffusion rates. These results disagree with the predictions of the perturbative renormalization group method.

cond-mat.stat-mech↗
arXiv2004

Critical behavior of the two dimensional 2A->3A, 4A->0 binary system

The phase transitions of the recently introduced 2A -> 3A, 4A -> 0 reaction-diffusion model (G.Odor, PRE 69 036112 (2004)) are explored in two dimensions. This model exhibits site occupation restriction and explicit diffusion of isolated particles. A reentrant phase diagram in the diffusion - creation rate space is confirmed in agreement with cluster mean-field and one-dimensional results. For strong diffusion a mean-field transition can be observed at zero branching rate characterized by $α=1/3$ density decay exponent. In contrast with this for weak diffusion the effective 2A ->3A->4A->0 reaction becomes relevant and the mean-field transition of the 2A -> 3A, 2A -> 0 model characterized by $α=1/2$ also appears for non-zero branching rates.

cond-mat.stat-mech↗
arXiv2004

Phase transitions of the binary production 2A->3A, 4A->0 model

Phase transitions of the 2A-> 3A, 4A->0 reaction-diffusion model is explored by dynamical, N-cluster approximations and by simulations.The model exhibits site occupation restriction and explicit diffusion of isolated particles. While the site mean-field approximation shows a single transition at zero branching rate introduced in PRE {\bf 67}, 016111 (2003), N>2 cluster approximations predict the appearance of another (reentrant) transition line for weak diffusion (D). This latter phase transition is continuous, occurs at finite branching rate and exhibits different scaling behavior. I show that the universal behavior of this transition is in agreement with that of the PCPD model both on the mean-field level and in one dimension. Therefore this model exhibiting annihilation by quadruplets does not fit in the recently suggested classification of universality classes of absorbing state transitions in one dimension (PRL {\bf 90}, 125701 (2003)). For high diffusion rates the effective 2A->3A->4A->0 reaction becomes irrelevant and the model exhibits a mean-field transition only. The two regions are separated by a non-trivial critical endpoint at D*.

cond-mat.stat-mech↗
arXiv2003

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.

cond-mat.stat-mech↗
arXiv2003

Universality classes in nonequilibrium lattice systems

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.

cond-mat.stat-mech↗