arXiv subjects

Haye Hinrichsen

Publications and source records attributed to Haye Hinrichsen.

At least 91 records · Page 5Linked to original sources

arXiv2001

Binary spreading process with parity conservation

Recently there has been a debate concerning the universal properties of the phase transition in the pair contact process with diffusion (PCPD) $2A\to 3A, 2A\to \emptyset$. Although some of the critical exponents seem to coincide with those of the so-called parity-conserving universality class, it was suggested that the PCPD might represent an independent class of phase transitions. This point of view is motivated by the argument that the PCPD does not conserve parity of the particle number. In the present work we pose the question what happens if the parity conservation law is restored. To this end we consider the the reaction-diffusion process $2A\to 4A, 2A\to \emptyset$. Surprisingly this process displays the same type of critical behavior, leading to the conclusion that the most important characteristics of the PCPD is the use of binary reactions for spreading, regardless of whether parity is conserved or not.

cond-mat.stat-mech↗

arXiv2001

Critical Coarsening without Surface Tension: the Voter Universality Class

We show that the two-dimensional voter model, usually considered to only be a marginal coarsening system, represents a broad class of models for which phase-ordering takes place without surface tension. We argue that voter-like growth is generically observed at order-disorder nonequilibrium transitions solely driven by interfacial noise between dynamically symmetric absorbing states.

cond-mat.stat-mech↗

arXiv2000

Exact solution of a reaction-diffusion process with three-site interactions

The one-dimensional reaction diffusion process AA->A and A0A->AAA is exactly solvable through the empty interval method if the diffusion rate equals the coagulation rate. Independently of the particle production rate, the model is always in the universality class of diffusion-annihilation. This allows us to check analytically the universality of finite-size scaling in a non-equilibrium critical point.

cond-mat.stat-mech↗

arXiv2000

Pair contact process with diffusion - A new type of nonequilibrium critical behavior?

Recently Carlon et. al. investigated the critical behavior of the pair contact process with diffusion [cond-mat/9912347]. Using density matrix renormalization group methods, they estimate the critical exponents, raising the possibility that the transition might belong to the same universality class as branching annihilating random walks with even numbers of offspring. This is surprising since the model does not have an explicit parity-conserving symmetry. In order to understand this contradiction, we estimate the critical exponents by Monte Carlo simulations. The results suggest that the transition might belong to a different universality class that has not been investigated before.

cond-mat.stat-mech↗

arXiv2000

First order phase transition with a logarithmic singularity in a model with absorbing states

Recently, Lipowski [cond-mat/0002378] investigated a stochastic lattice model which exhibits a discontinuous transition from an active phase into infinitely many absorbing states. Since the transition is accompanied by an apparent power-law singularity, it was conjectured that the model may combine features of first- and second-order phase transitions. In the present work it is shown that this singularity emerges as an artifact of the definition of the model in terms of products. Instead of a power law, we find a logarithmic singularity at the transition. Moreover, we generalize the model in such a way that the second-order phase transition becomes accessible. As expected, this transition belongs to the universality class of directed percolation.

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arXiv2000

On the microcanonical solution of a system of globally coupled rotators

We study the Hamiltonian Mean Field (HMF) model, a system of $N$ fully coupled particles, in the microcanonical ensemble. We use the previously obtained free energy in the canonical ensemble to derive entropy as a function of energy, using Legendre transform techniques. The temperature-energy relation is found to coincide with the one obtained in the canonical ensemble and includes a {\it metastable} branch which represents spatially homogeneous states below the critical energy. "Water bag" states, with removed tails momentum distribution, lying on this branch, are shown to relax to equilibrium on a time which diverges linearly with $N$ in an energy region just below the phase transition.

cond-mat↗

arXiv2000

First-order transitions in fluctuating 1+1-dimensional nonequilibrium systems

We demonstrate that first-order phase transitions in 1+1-dimensional nonequilibrium systems with fluctuating ordered phases are impossible, provided that there are no additional conservation laws, long-range interactions, macroscopic currents, or special boundary conditions. Since minority islands in the ordered phase of such systems can only shrink by short-range interactions, it is impossible to stabilize a fluctuating ordered state. The apparent first-order behavior turns out to be a transient phenomenon, crossing over to a continuous transition after very long time. As examples we consider the triplet creation model 3X->4X, X->O, the annihilation/fission process 2X->3X, 2X->O, as well as spreading on a diffusing background X+Y->2Y, Y->X.

cond-mat.stat-mech↗

arXiv2000

Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States

This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic nonequilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.

cond-mat.stat-mech↗

arXiv2000

Cyclically coupled spreading and pair annihilation

Recently it has been shown that the transition of the 1+1-dimensional annihilation-fission process 2X->3X, 2X->0 exhibits an unusual type of nonequilibrium critical behavior. The phenomenological properties of critical clusters are characterized by two different dynamic modes for spreading and diffusion. In order to describe the interplay of these modes, we introduce an effective model which involves two species of particles A and B. The A-particles perform an ordinary directed percolation process while the B particles diffuse and annihilate. Both subsystems are cyclically coupled by particle transmutation A <-> B. The resulting critical behavior is in many respects similar to the one observed in the annihilation-fission process.

cond-mat.stat-mech↗

arXiv1999

On possible experimental realizations of directed percolation

Directed percolation is one of the most prominent universality classes of nonequilibrium phase transitions and can be found in a large variety of models. Despite its theoretical success, no experiment is known which clearly reproduces the critical exponents of directed percolation. The present work compares suggested experiments and discusses possible reasons why the observation of the critical exponents of directed percolation is obscured or even impossible.

cond-mat.stat-mech↗

arXiv1999

Flowing sand - a physical realization of Directed Percolation

We introduce and investigate a simple model to describe recent experiments by Douady and Daerr on flowing sand. The model reproduces experimentally observed compact avalanches, whose opening angle decreases linearly as a threshold is approached. On large scales the model exhibits a crossover from compact directed percolation to directed percolation; we predict similar behavior for the experimental system. We estimate the regime where "true" directed percolation morphology and exponents will be observed, providing the first experimental realization for this class of models.

cond-mat.stat-mech↗

arXiv1999

Flowing sand - a possible physical realization of Directed Percolation

A simple model for flowing sand on an inclined plane is introduced. The model is related to recent experiments by Douady and Daerr [Nature 399, 241 (1999)] and reproduces some of the experimentally observed features. Avalanches of intermediate size appear to be compact, placing the critical behavior of the model into the universality class of compact directed percolation. On very large scales, however, the avalanches break up into several branches leading to a crossover from compact to ordinary directed percolation. Thus, systems of flowing granular matter on an inclined plane could serve as a first physical realization of directed percolation.

cond-mat.stat-mech↗

arXiv1999

First order phase transition in a 1+1-dimensional nonequilibrium wetting process

A model for nonequilibrium wetting in 1+1 dimensions is introduced. It comprises adsorption and desorption processes with a dynamics which generically does not obey detailed balance. Depending on the rates of the dynamical processes the wetting transition is either of first or second order. It is found that the wet (unbound) and the non-wet (pinned) states coexist and are both thermodynamically stable in a domain of the dynamical parameters which define the model. This is in contrast with equilibrium transitions where coexistence of thermodynamically stable states takes place only on the transition line.

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.

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arXiv1998

A model for anomalous directed percolation

We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability distribution for long-range infections which decays in $d$ spatial dimensions as $1/r^{d+σ}$. Extensive numerical simulations are performed in order to determine the density exponent $β$ and the correlation length exponents $ν_{||}$ and $ν_\perp$ for various values of $σ$. We observe that these exponents vary continuously with $σ$, in agreement with recent field-theoretic predictions. We also study a model for pairwise annihilation of particles with algebraically distributed long-range interactions.

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arXiv1998

Scaling Laws and Topological Exponents in Voronoi Tessellations of Intermittent Point Distributions

Voronoi tessellations of scale-invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures. As an example we analyze Voronoi diagrams of intermittent particle distributions generated by a directed percolation process in (2+1) dimensions. We observe that the average area of a cell increases much faster with the number of its neighbours than in natural cellular structures where Lewis' law predicts a linear behaviour. We propose and numerically verify a universal scaling law that relates shape and size of the cells in scale-invariant tessellations. A novel exponent, related to the topological properties of the tessellation, is introduced and estimated numerically.

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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