arXiv subjects

Haye Hinrichsen

Publications and source records attributed to Haye Hinrichsen.

At least 73 records · Page 4Linked to original sources

arXiv2005

The phase transition of the diffusive pair contact process revisited

The restricted diffusive pair contact process 2A->3A, 2A->0 (PCPD) and the classification of its critical behavior continues to be a challenging open problem of non-equilibrium statistical mechanics. Recently Kockelkoren and Chate [Phys. Rev. Lett. 90, 125701 (2003)] suggested that the PCPD in one spatial dimension represents a genuine universality class of non-equilibrium phase transitions which differs from previously known classes. To this end they introduced an efficient lattice model in which the number of particles per site is unrestricted. In numerical simulations this model displayed clean power laws, indicating ordinary critical behavior associated with certain non-trivial critical exponents. In the present work, however, we arrive at a different conclusion. Increasing the numerical effort, we find a slow drift of the effective exponents which is of the same type as observed in previously studied fermionic realizations. Analyzing this drift we discuss the possibility that the asymptotic critical behavior of the PCPD may be governed by an ordinary directed percolation fixed point.

cond-mat.stat-mech↗

arXiv2004

Spreading with immunization in high dimensions

We investigate a model of epidemic spreading with partial immunization which is controlled by two probabilities, namely, for first infections, $p_0$, and reinfections, $p$. When the two probabilities are equal, the model reduces to directed percolation, while for perfect immunization one obtains the general epidemic process belonging to the universality class of dynamical percolation. We focus on the critical behavior in the vicinity of the directed percolation point, especially in high dimensions $d>2$. It is argued that the clusters of immune sites are compact for $d\leq 4$. This observation implies that a recently introduced scaling argument, suggesting a stretched exponential decay of the survival probability for $p=p_c$, $p_0\ll p_c$ in one spatial dimension, where $p_c$ denotes the critical threshold for directed percolation, should apply in any dimension $d \leq 3$ and maybe for $d=4$ as well. Moreover, we show that the phase transition line, connecting the critical points of directed percolation and of dynamical percolation, terminates in the critical point of directed percolation with vanishing slope for $d<4$ and with finite slope for $d\geq 4$. Furthermore, an exponent is identified for the temporal correlation length for the case of $p=p_c$ and $p_0=p_c-ε$, $ε\ll 1$, which is different from the exponent $ν_\parallel$ of directed percolation. We also improve numerical estimates of several critical parameters and exponents, especially for dynamical percolation in $d=4,5$.

cond-mat.stat-mech↗

arXiv2004

Mean field theory for skewed height profiles in KPZ growth processes

We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the influence of the nonlinear term in the KPZ equation into account. Although spatial correlations are neglected, the mean field equations still reflect the spatial dimensionality of the system. In the special case of Edwards-Wilkinson growth,our mean field theory correctly reproduces all features. In the presence of a nonlinear term one observes a crossover to a KPZ-like behavior with the correct dynamical exponent $z=3/2$. In particular we compute the skewed interface profile during roughening, and we study the influence of a co-moving reflecting wall, which has been discussed recently in the context of nonequilibrium wetting and synchronization transitions. Also here the mean field approximation reproduces all qualitative features of the full KPZ equation, although with different values of the surface exponents.

cond-mat.stat-mech↗

arXiv2004

The non-equilibrium phase transition of the pair-contact process with diffusion

The pair-contact process 2A->3A, 2A->0 with diffusion of individual particles is a simple branching-annihilation processes which exhibits a phase transition from an active into an absorbing phase with an unusual type of critical behaviour which had not been seen before. Although the model has attracted considerable interest during the past few years it is not yet clear how its critical behaviour can be characterized and to what extent the diffusive pair-contact process represents an independent universality class. Recent research is reviewed and some standing open questions are outlined.

cond-mat.stat-mech↗

arXiv2004

Agglomeration of Oppositely Charged Particles in Nonpolar Liquids

We study the aggregation of insulating electrically charged spheres suspended in a nonpolar liquid. Regarding the van der Waals interaction as an irreversible sticking force, we are especially interested in the charge distribution after aggregation. Solving the special case of two oppositely charged particles exactly, it is shown that the surface charges either recombine or form a residual dipole, depending on the initial condition. The theoretical findings are compared with numerical results from Monte Carlo simulations.

physics.class-ph↗

arXiv2003

Epidemic processes with immunization

We study a model of directed percolation (DP) with immunization, i.e. with different probabilities for the first infection and subsequent infections. The immunization effect leads to an additional non-Markovian term in the corresponding field theoretical action. We consider immunization as a small perturbation around the DP fixed point in d<6, where the non-Markovian term is relevant. The immunization causes the system to be driven away from the neighbourhood of the DP critical point. In order to investigate the dynamical critical behaviour of the model, we consider the limits of low and high first infection rate, while the second infection rate remains constant at the DP critical value. Scaling arguments are applied to obtain an expression for the survival probability in both limits. The corresponding exponents are written in terms of the critical exponents for ordinary DP and DP with a wall. We find that the survival probability does not obey a power law behaviour, decaying instead as a stretched exponential in the low first infection probability limit and to a constant in the high first infection probability limit. The theoretical predictions are confirmed by optimized numerical simulations in 1+1 dimensions.

cond-mat.stat-mech↗

arXiv2003

Epidemic spreading with immunization and mutations

The spreading of infectious diseases with and without immunization of individuals can be modeled by stochastic processes that exhibit a transition between an active phase of epidemic spreading and an absorbing phase, where the disease dies out. In nature, however, the transmitted pathogen may also mutate, weakening the effect of immunization. In order to study the influence of mutations, we introduce a model that mimics epidemic spreading with immunization and mutations. The model exhibits a line of continuous phase transitions and includes the general epidemic process (GEP) and directed percolation (DP) as special cases. Restricting to perfect immunization in two spatial dimensions we analyze the phase diagram and study the scaling behavior along the phase transition line as well as in the vicinity of the GEP point. We show that mutations lead generically to a crossover from the GEP to DP. Using standard scaling arguments we also predict the form of the phase transition line close to the GEP point. It turns out that the protection gained by immunization is vitally decreased by the occurrence of mutations.

cond-mat.stat-mech↗

arXiv2003

The diffusive pair contact process and non-equilibrium wetting

The Langevin equation for the pair contact process with diffusion (PCPD) 2A->3A, 2A->0 can be mapped by a Cole-Hopf transformation to a Kardar-Parisi-Zhang equation in a potential which has been discussed previously in the context of non-equilibrium wetting. Using this transformation the phase transition in the PCPD manifests itself as a depinning transition at the borderline of a region of phase coexistence, supporting the conjecture that the PCPD belongs to the DP universality class.

cond-mat.stat-mech↗

arXiv2002

On generalized scaling laws with continuously varying exponents

Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the parameters. However, some systems do not obey power-law scaling, instead there is numerical evidence for a logarithmic scaling form, in which the scaling function depends on ratios of the logarithms of the parameters. Based on previous ideas by C. Tang we propose that this type of logarithmic scaling can be explained by a concept of local scaling invariance with continuously varying exponents. The functional dependence of the exponents is constrained by a homomorphism, which can be expressed as a set of partial differential equations. Solving these equations we obtain logarithmic scaling as a special case. The other solutions lead to scaling forms where logarithmic and power-law scaling are mixed.

cond-mat.stat-mech↗

arXiv2002

Roughening transition driven by a binary spreading process

We introduce a solid-on-solid growth process which evolves by random deposition of dimers, surface diffusion, and evaporation of monomers from the edges of plateaus. It is shown that the model exhibits a robust transition from a smooth to a rough phase. The roughening transition is driven by an absorbing phase transition at the bottom layer of the interface, which displays the same type of critical behavior as the pair contact process with diffusion 2A->3A, 2A->0.

cond-mat.stat-mech↗

arXiv2002

Logarithmic roughening in a growth process with edge evaporation

Roughening transitions are often characterized by unusual scaling properties. As an example we investigate the roughening transition in a solid-on-solid growth process with edge evaporation [Phys. Rev. Lett. 76, 2746 (1996)], where the interface is known to roughen logarithmically with time. Performing high-precision simulations we find appropriate scaling forms for various quantities. Moreover we present a simple approximation explaining why the interface roughens logarithmically.

cond-mat.stat-mech↗

arXiv2002

Stochastic cellular automaton for the coagulation-fission-process 2A->3A, 2A->A

We introduce an efficient cellular automaton for the coagulation-fission process with diffusion 2A->3A, 2A->A in arbitrary dimensions. As the well-known Domany-Kinzel model, it is defined on a tilted hypercubic lattice and evolves by parallel updates. The model exhibits a non-equilibrium phase transition from an active into an absorbing phase and its critical properties are expected to be of the same type as in the pair contact process with diffusion. High-precision simulations on a parallel computer suggest that various quantities of interest do not show the expected power-law scaling, calling for new approaches to understand this unusual type of critical behavior.

cond-mat.stat-mech↗

arXiv2002

Phase transition in a triplet process

We show that the reaction-diffusion process 3A -> 4A, 3A -> 2A exhibits a different type of continuous phase transition from an active into an absorbing phase. Because of the upper critical dimension d_c = 4/3 we expect the phase transition in 1+1 dimensions to be characterized by non-trivial fluctuation effects.

cond-mat.stat-mech↗

arXiv2002

Quantum Dimensional Zeeman Effect in the Magneto-optical Absorption Spectrum for Quantum Dot - Impurity Center Systems

Magneto-optical properties of the quantum dot - impurity center (QD-IC) systems synthesized in a transparent dielectric matrix are considered. For the QD one-electron state description the parabolic model of the confinement potential is used. Within the framework of zero-range potential model and the effective mass approach, the light impurity absorption coefficient for the case of transversal polarization with respect to the applied magnetic field direction, with consideration of the QD size dispersion, has been analytically calculated. It is shown that for the case of transversal polarization the light impurity absorption spectrum is characterized by the quantum dimensional Zeeman effect.

cond-mat.str-el↗

arXiv2002

Yang-Lee zeros for a nonequilibrium phase transition

Equilibrium systems which exhibit a phase transition can be studied by investigating the complex zeros of the partition function. This method, pioneered by Yang and Lee, has been widely used in equilibrium statistical physics. We show that an analogous treatment is possible for a nonequilibrium phase transition into an absorbing state. By investigating the complex zeros of the survival probability of directed percolation processes we demonstrate that the zeros provide information about universal properties. Moreover we identify certain non-trivial points where the survival probability for bond percolation can be computed exactly.

cond-mat.stat-mech↗

arXiv2001

Multifractal current distribution in random diode networks

Recently it has been shown analytically that electric currents in a random diode network are distributed in a multifractal manner [O. Stenull and H. K. Janssen, Europhys. Lett. 55, 691 (2001)]. In the present work we investigate the multifractal properties of a random diode network at the critical point by numerical simulations. We analyze the currents running on a directed percolation cluster and confirm the field-theoretic predictions for the scaling behavior of moments of the current distribution. It is pointed out that a random diode network is a particularly good candidate for a possible experimental realization of directed percolation.

cond-mat.stat-mech↗

arXiv2001

Directed Percolation and the Golden Ratio

Applying the theory of Yang-Lee zeros to nonequilibrium critical phenomena, we investigate the properties of a directed bond percolation process for a complex percolation parameter p. It is shown that for the Golden Ratio p=(1(+/-)sqrt(5))/2 and for p=2 the survival probability of a cluster can be computed exactly.

cond-mat.stat-mech↗

arXiv2001

Unusual scaling for pulsed laser deposition

We demonstrate that a simple model for pulsed laser deposition exhibits an unusual type of scaling behavior for the island density in the submonolayer regime. This quantity is studied as function of pulse intensity and deposition time. We find a data collapse for the ratios of the logarithms of these quantities, whereas conventional scaling as observed in molecular beam epitaxy involves ratios of powers.

cond-mat.stat-mech↗