Zoltán Rácz

Eötvös Loránd University, Budapest, Budapest fovaros, Hungary

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Publications (52)157.12 Total impact

  • Source
    L. O'Malley · B. Kozma · G. Korniss · Z. Racz · T Caraco
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    ABSTRACT: We consider an individual-based two-dimensional spatial model with nearest-neighbor preemptive competition to study front propagation between an invader and a resident species. In particular, we investigate the asymptotic front velocity and compare it with mean-field predictions. 1.1 Introduction and Model The dynamics of propagating fronts are fundamental in the study of the spread of advantageous alleles, species [1], or opinions [2]. Most notably, Fisher [3] and Kolmogorov et al. [4] first addressed the velocity characteristics of a simple front by way of a reaction-diffusion equation [1], which
    Full-text · Chapter · Dec 2007
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    ABSTRACT: We report on the morphological instabilities of the liquid-liquid interface in a liquid crystal at a nematic-smectic transition. Upon increasing the undercooling of the nematic phase, the following sequence of distinct structures was observed: dense branching fingers, dendrites, and dense branching fronts. We have determined the characteristic length scales and growth velocities of these patterns.
    No preview · Article · Jul 2007 · EPL (Europhysics Letters)
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    L O'Malley · B Kozma · G Korniss · Z Rácz · T Caraco
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    ABSTRACT: We study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits an effective power-law dependence on the difference between the two species' clonal propagation rates (key ecological parameters). The mean-field approximation behaves similarly, but the power law's exponent slightly differs from the individual-based model's result. We also study roughening of the front, using the framework of nonequilibrium interface growth. Our analysis indicates that initially flat, linear invading fronts exhibit Kardar-Parisi-Zhang (KPZ) roughening in one transverse dimension. Further, this finding implies, and is also confirmed by simulations, that the temporal correction to the asymptotic front velocity is of O(t(-2/3)).
    Full-text · Article · Nov 2006 · Physical Review E
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    V. Eisler · Ö Legeza · Z. Racz
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    ABSTRACT: The zero-temperature XX chain is studied with emphasis on the properties of a block of $L$ spins inside the chain. We investigate the quantum fluctuations resulting from the entanglement of the block with the rest of the chain using analytical as well as numerical (density matrix renormalization group) methods. It is found that the rest of the chain acts as a thermal environment and an effective temperature can be introduced to describe the fluctuations. We show that the effective temperature description is robust in the sense that several independent definitions (through fluctuation dissipation theorem, comparing with a finite temperature system) yield the same functional form in the limit of large block size ($L\to\infty$). The effective temperature can also be shown to satisfy the basic requirements on how it changes when two bodies of equal or unequal temperatures are brought into contact. Comment: 19 pages, 7 figures
    Preview · Article · Sep 2006 · Journal of Statistical Mechanics Theory and Experiment
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    H Guclu · G Korniss · MA Novotny · Z Toroczkai · Z Rácz
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    ABSTRACT: Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by "simulating the simulations," based on the exact algorithmic rules, supported by coarse-grained arguments.
    Full-text · Article · Jun 2006 · Physical Review E
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    Z. Rácz
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    ABSTRACT: Nonequilibrium phase transitions are discussed with emphasis on general features such as the role of detailed balance violation in generating effective (long-range) interactions, the importance of dynamical anisotropies, the connection between various mechanisms generating power-law correlations, and the emergence of universal distribution functions for macroscopic quantities. Quantum spin chains are also discussed in order to demonstrate how to construct steady-states carrying fluxes in quantum systems, and to explain how the fluxes may generate power-law correlations.
    Preview · Chapter · Feb 2004
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    E Marinari · A Pagnani · G Parisi · Z Rácz
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    ABSTRACT: Simulations of restricted solid-on-solid growth models are used to build the width distributions of $d=2\char21{}5$ dimensional Kardar-Parisi-Zhang (KPZ) interfaces. We find that the universal scaling function associated with the steady-state width distribution changes smoothly as d is increased, thus strongly suggesting that $d=4$ is not an upper critical dimension for the KPZ equation. The dimensional trends observed in the scaling functions indicate that the upper critical dimension is at infinity.
    Preview · Article · Mar 2002 · Physical Review E
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    ABSTRACT: We consider the single-particle velocity distribution of a one-dimensional fluid of inelastic particles. Both the freely evolving (cooling) system and the non-equilibrium stationary state obtained in the presence of random forcing are investigated, and special emphasis is paid to the small inelasticity limit. The results are obtained from analytical arguments applied to the Boltzmann equation along with three complementary numerical techniques (Molecular Dynamics, Direct Monte Carlo Simulation Methods and iterative solutions of integro-differential kinetic equations). For the freely cooling fluid, we investigate in detail the scaling properties of the bimodal velocity distribution emerging close to elasticity and calculate the scaling function associated with the distribution function. In the heated steady state, we find that, depending on the inelasticity, the distribution function may display two different stretched exponential tails at large velocities. The inelasticity dependence of the crossover velocity is determined and it is found that the extremely high velocity tail may not be observable at ``experimentally relevant'' inelasticities. Comment: Latex, 14 pages, 12 eps figures
    Full-text · Article · Oct 2001 · Journal of Physics A General Physics
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    U.C. Täuber · J.E. Santos · Z. Rácz
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    ABSTRACT: Phase transitions in non-equilibrium steady states of O(n)-symmetric models with reversible mode couplings are studied using dynamic field theory and the renormalization group. The systems are driven out of equilibrium by dynamical anisotropy in the noise for the conserved quantities, i.e., by constraining their diffusive dynamics to be at different temperatures and in - and -dimensional subspaces, respectively. In the case of the Sasvári-Schwabl-Szépfalusy (SSS) model for planar ferro- and isotropic antiferromagnets, we assume a dynamical anisotropy in the noise for the non-critical conserved quantities that are dynamically coupled to the non-conserved order parameter. We find the equilibrium fixed point (with isotropic noise) to be stable with respect to these non-equilibrium perturbations, and the familiar equilibrium exponents therefore describe the asymptotic static and dynamic critical behavior. Novel critical features are only found in extreme limits, where the ratio of the effective noise temperatures is either zero or infinite. On the other hand, for model J for isotropic ferromagnets with a conserved order parameter, the dynamical noise anisotropy induces effective long-range elastic forces, which lead to a softening only of the -dimensional sector in wavevector space with lower noise temperature . The ensuing static and dynamic critical behavior is described by power laws of a hitherto unidentified universality class, which, however, is not accessible by perturbational means for .We obtain formal expressions for the novel critical exponents in a double expansion about the static and dynamic upper critical dimensions and , i.e., about the equilibrium theory.
    Full-text · Article · Dec 1998 · Physics of Condensed Matter
  • Huang-Jian Xu · B Bergersen · Z Racz
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    ABSTRACT: Monte Carlo simulations are presented for Ising dipoles on body centred cubic and tetragonal lattices. A finite size scaling form that includes logarithmic corrections is proposed and found to significantly improve the data collapse. With lattice parameters appropriate to LiHoF4 the authors obtain a ferromagnetic transition temperature Tc=1.51 K in good agreement with experiment.
    No preview · Article · Dec 1998 · Journal of Physics Condensed Matter
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    ABSTRACT: The ordering properties of Ising dipoles are studied in mean field theory, and by Monte Carlo simulations. The boundary conditions are such that there is no net depolarizing field and both regular lattices and various random arrangements are considered. In the mean field approach the authors employ the replica method with a Gaussian approximation for the distribution of dipole-dipole interactions, while a Kirkwood approximation is used for the spatial distribution of dipoles. The low-temperature phase for a system of randomly parked dipoles and diluted face centred cubic and body centred cubic lattices is found to be ferro-electric above a critical concentration. Below this concentration the mean field theory predicts a spin glass. The simulations are only carried out for the body centred cubic lattice. The transition temperature to the ferroelectric state is determined from finite size scaling of the mean square polarization. The critical concentration for the occurrence of a spin glass phase is estimated by zero temperature Monte Carlo simulations using the simulated annealing method. The results are found to be in qualitative agreement with those of the mean field theory described above.
    No preview · Article · Dec 1998 · Journal of Physics Condensed Matter
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    Tibor Antal · Zoltán Rácz
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    ABSTRACT: Edwards--Wilkinson type models are studied in 1+1 dimensions and the time-dependent distribution, P_L(w^2,t), of the square of the width of an interface, w^2, is calculated for systems of size L. We find that, using a flat interface as an initial condition, P_L(w^2,t) can be calculated exactly and it obeys scaling in the form <w^2>_\infty P_L(w^2,t) = Phi(w^2 / <w^2>_\infty, t/L^2) where <w^2>_\infty is the stationary value of w^2. For more complicated initial states, scaling is observed only in the large- time limit and the scaling function depends on the initial amplitude of the longest wavelength mode. The short-time limit is also interesting since P_L(w^2,t) is found to closely approximate the log-normal distribution. These results are confirmed by Monte Carlo simulations on a `roof-top' model of surface evolution. Comment: 5 pages, latex, 3 ps figures in a separate files, submitted to Phys.Rev.E
    Preview · Article · Oct 1996 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
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    Birger Bergersen · Zoltán Rácz · HJ Xu
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    ABSTRACT: Two-spin correlations generated by interactions that decay with distance r as r-1-sigma with -10 that can be observed by introducing magnified correlations LC(r,L)-tsumrC(r,L). The magnified correlations are shown to have a scaling form Phi(r/L), and the singular structure of Phi(x) for x-->0 is found to be the same at all temperatures, including the critical point. These conclusions are supported by the results of Monte Carlo simulations for systems with sigma=-0.50 and -0.25 both at the critical temperature T=Tc and at T=2Tc. (c) 1995 The American Physical Society
    Full-text · Article · Jan 1996 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • Zoltán Rácz · Michael Plischke
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    ABSTRACT: Nonequilibrium growth processes are frequently characterized by the width w(L,t) of the active zone, where t is the time elapsed since the start of the process and L is the spatial interval over which the measurement is carried out. Quite generally, w(L,t) obeys a scaling form w(L,t)~Lzetaf(tL-z), and many workers have attempted to determine the dynamic universality class of such processes by a measurement of the exponents zeta and z. In this paper, we calculate the steady-state width distribution P(w2) for several three-dimensional growth processes and show that, expressed in a suitable form, P(w2) can be used to distinguish between different possible universality classes. We also reanalyze experimental data obtained by scanning-tunneling or atomic-force microscopy and show that P(w2) provides valuable information on the nature of a growth process.
    No preview · Article · Dec 1994 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • M Plischke · Z Rácz · RK Zia
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    ABSTRACT: One-dimensional interfaces with curvature-driven growth kinetics are investigated. We calculate the steady-state distribution P(w2) of the square of the width of the interface w2 and show that, as in the case for random-walk interfaces, the result can be written in a scaling form P(w2)=Phi(w2/), where is the average of w2. The scaling function Phi(x) is found to be distinct from that of random-walk interfaces, but, as our Monte Carlo simulations indicate, this function is universal for curvature-driven growth. It is argued that comparison of scaling functions can be a useful method for distinguishing between universality classes of growth processes.
    No preview · Article · Dec 1994 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • Kevin E. Bassler · Zoltán Rácz
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    ABSTRACT: The phase diagram of a two-temperature kinetic Ising model which evolves by Kawasaki dynamics is studied using Monte Carlo simulations in dimension d=2 and solving mean-spherical approximation in general d. We show that the equal-temperature (equilibrium) Ising critical point is a bicritical point where two nonequilibrium critical lines meet a first-order line separating two distinct ordered phases. The shape of the nonequilibrium critical lines is described by a crossover exponent, phi, which we find to be equal to the susceptibility exponent, gamma, of the Ising model.
    No preview · Article · Oct 1994 · Physical Review Letters
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    ABSTRACT: Roughening of a one-dimensional interface is studied under the assumption that the interface configurations are continuous, periodic random walks. The distribution of the square of the width of interface, [ital w][sup 2], is found to scale as [ital P]([ital w][sup 2])=[l angle][ital w][sup 2][r angle][sup [minus]1][Phi]([ital w][sup 2]/[l angle][ital w][sup 2][r angle]) where [l angle][ital w][sup 2][r angle] is the average of [ital w][sup 2]. We calculate the scaling function [Phi]([ital x]) exactly and compare it both to exact enumerations for a discrete-slope surface evolution model and to [Phi]'s obtained in Monte Carlo simulations of equilibrium and driven interfaces of chemically reacting systems.
    No preview · Article · Sep 1994 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • Z Rácz · R.K.P. Zia
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    ABSTRACT: We study the nonequilibrium properties of a one-dimensional kinetic Ising model in which spins interact by nearest-neighbor ferromagnetic interactions and a spin-flip dynamics is generated by contact with heat baths that are at different temperatures on even and odd lattice sites. The average energy (ɛ) and the energy flux between the two sublattices (jɛ) are calculated exactly and the two-spin steady-state correlations are expressed through ɛ and jɛ. It is found that the correlations can be classified as ferromagnetic (for ɛ<0 and jɛ small), antiferromagnetic (ɛ>0, jɛ small), oscillating ferromagnetic (ɛ<0, jɛ large), and oscillating antiferromagnetic (ɛ>0, jɛ large). We also find a disorder line (ɛ=0, jɛ arbitrary) on which all correlations are zero. The character of spatial correlations is shown to be reflected in the time evolution of sublattice magnetizations: The dynamics is purely relaxational in the ferromagnetic and antiferromagnetic regime while it is damped oscillatory in the oscillating ferromagnetic and antiferromagnetic regions.
    No preview · Article · Feb 1994 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • HJ Xu · Birger Bergersen · Zoltán Rácz
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    ABSTRACT: A d=2 dimensional kinetic Ising model that evolves by a combination of spin flips and spin exchanges is investigated. The spin flips satisfy detailed balance for the equilibrium state of the Ising model at temperature T while the spin exchanges are random Lévy flights of dimension sigma=1.5. Our Monte Carlo (MC) simulations show that the steady state of this system displays a second-order phase transition as T is lowered. Comparing the critical fluctuations of the magnetization to those of an Ising model in which the interaction decays with distance as r-3.5, we find that, within the resolution of the MC data, the critical exponents and the scaling functions of the two systems coincide. We argue that this coincidence indicates that a recent conjecture about the random Lévy flights generating long-range interaction of the form Veff(r)~r-d-sigma is valid not only in the spherical limit and in d=1 but also in d=2.
    No preview · Article · Apr 1993 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • H Hayakawa · Z Rácz · T Tsuzuki
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    ABSTRACT: The growth kinetics following a quench from high temperatures to zero temperature is studied using the time-dependent Ginzburg-Landau model. We investigate d-dimensional systems with n-component order parameter and assume that the interactions decay with distance r as V(r) is similar to r(-d-sigma) with 0 < sigma < 2. The spherical limit (n = infinity) is solved for both conserved and nonconserved order-parameter dynamics and the scaling properties of the structure factor are calculated. We find scaling features (including multiscaling in the conserved case) that are similar to those of systems with short-range interactions. The essential difference is that the short-range value of the dynamic critical exponent z(s) is replaced by z = z(s) - 2 + sigma and the form of the scaling function is modified. We also study the general n case for non-conserved order-parameter dynamics and calculate the structure factor in an approximate scheme with the results that (i) the spherical-limit value of z remains unchanged as n is decreased down to n = 1 and (ii) the spatial correlations decay at large distances as r(-d-sigma).
    No preview · Article · Apr 1993 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Publication Stats

2k Citations
157.12 Total Impact Points

Institutions

  • 1973-2007
    • Eötvös Loránd University
      • Department of Theoretical Physics
      Budapest, Budapest fovaros, Hungary
  • 2006
    • Rensselaer Polytechnic Institute
      • Department of Physics, Applied Physics, and Astronomy
      Троя, New York, United States
  • 2001
    • Université Paris-Sud 11
      • Laboratoire de Physique Théorique d'Orsay
      Orsay, Île-de-France, France
  • 1987-1998
    • University of British Columbia - Vancouver
      • Department of Physics and Astronomy
      Vancouver, British Columbia, Canada
  • 1996
    • University of Manitoba
      Winnipeg, Manitoba, Canada
  • 1994
    • Virginia Polytechnic Institute and State University
      • Department of Physics
      Blacksburg, Virginia, United States
  • 1984-1994
    • Simon Fraser University
      • Department of Physics
      Burnaby, British Columbia, Canada
    • Sapienza University of Rome
      Roma, Latium, Italy
  • 1993
    • Tohoku University
      • Department of Physics
      Sendai, Kagoshima-ken, Japan
    • Clarkson University
      • Department of Physics
      Potsdam, NY, United States
  • 1989
    • Université de Genève
      • Department of Theoretical Physics
      Carouge, GE, Switzerland
  • 1983
    • Università degli Studi Europea di Roma
      Roma, Latium, Italy
  • 1975-1980
    • McMaster University
      Hamilton, Ontario, Canada