Influence of diffusion on models for non-equilibrium wetting

It is shown that the critical properties of a recently studied model for non-equilibrium wetting are robust if one extends the dynamic rules by single-particle diffusion on terraces of the wetting layer. Examining the behavior at the critical point and along the phase transition line, we identify a special point in the phase diagram where detailed balance of the dynamical processes is partially broken.Comment: 6 pages, 9 figure

On the predictive power of Local Scale Invariance

Local Scale Invariance (LSI) is a theory for anisotropic critical phenomena designed in the spirit of conformal invariance. For a given representation of its generators it makes non-trivial predictions about the form of universal scaling functions. In the past decade several representations have been identified and the corresponding predictions were confirmed for various anisotropic critical systems. Such tests are usually based on a comparison of two-point quantities such as autocorrelation and response functions. The present work highlights a potential problem of the theory in the sense that it may predict any type of two-point function. More specifically, it is argued that for a given two-point correlator it is possible to construct a representation of the generators which exactly reproduces this particular correlator. This observation calls for a critical examination of the predictive content of the theory.Comment: 17 pages, 2 eps figure

Maximal Localisation in the Presence of Minimal Uncertainties in Positions and Momenta

Small corrections to the uncertainty relations, with effects in the ultraviolet and/or infrared, have been discussed in the context of string theory and quantum gravity. Such corrections lead to small but finite minimal uncertainties in position and/or momentum measurements. It has been shown that these effects could indeed provide natural cutoffs in quantum field theory. The corresponding underlying quantum theoretical framework includes small `noncommutative geometric' corrections to the canonical commutation relations. In order to study the full implications on the concept of locality it is crucial to find the physical states of then maximal localisation. These states and their properties have been calculated for the case with minimal uncertainties in positions only. Here we extend this treatment, though still in one dimension, to the general situation with minimal uncertainties both in positions and in momenta.Comment: Latex, 21 pages, 2 postscript figure

Universality class of the pair contact process with diffusion

The pair contact process with diffusion (PCPD) is studied with a standard Monte Carlo approach and with simulations at fixed densities. A standard analysis of the simulation results, based on the particle densities or on the pair densities, yields inconsistent estimates for the critical exponents. However, if a well-chosen linear combination of the particle and pair densities is used, leading corrections can be suppressed, and consistent estimates for the independent critical exponents delta=0.16(2), beta=0.28(2) and z=1.58 are obtained. Since these estimates are also consistent with their values in directed percolation (DP), we conclude that PCPD falls in the same universality class as DP.Comment: 8 pages, 8 figures, accepted by Phys. Rev. E (not yet published

A precise approximation for directed percolation in d=1+1

We introduce an approximation specific to a continuous model for directed percolation, which is strictly equivalent to 1+1 dimensional directed bond percolation. We find that the critical exponent associated to the order parameter (percolation probability) is beta=(1-1/\sqrt{5})/2=0.276393202..., in remarkable agreement with the best current numerical estimate beta=0.276486(8).Comment: 4 pages, 3 EPS figures; Submitted to Physical Review Letters v2: minor typos + 1 major typo in Eq. (30) correcte

In an Ising model with spin-exchange dynamics damage always spreads

We investigate the spreading of damage in Ising models with Kawasaki spin-exchange dynamics which conserves the magnetization. We first modify a recent master equation approach to account for dynamic rules involving more than a single site. We then derive an effective-field theory for damage spreading in Ising models with Kawasaki spin-exchange dynamics and solve it for a two-dimensional model on a honeycomb lattice. In contrast to the cases of Glauber or heat-bath dynamics, we find that the damage always spreads and never heals. In the long-time limit the average Hamming distance approaches that of two uncorrelated systems. These results are verified by Monte-Carlo simulations.Comment: 5 pages REVTeX, 4 EPS figures, final version as publishe

Differences between regular and random order of updates in damage spreading simulations

We investigate the spreading of damage in the three-dimensional Ising model by means of large-scale Monte-Carlo simulations. Within the Glauber dynamics we use different rules for the order in which the sites are updated. We find that the stationary damage values and the spreading temperature are different for different update order. In particular, random update order leads to larger damage and a lower spreading temperature than regular order. Consequently, damage spreading in the Ising model is non-universal not only with respect to different update algorithms (e.g. Glauber vs. heat-bath dynamics) as already known, but even with respect to the order of sites.Comment: final version as published, 4 pages REVTeX, 2 eps figures include

Criticality and oscillatory behavior in non-Markovian Contact Process

A Non-Markovian generalization of one-dimensional Contact Process (CP) is being introduced in which every particle has an age and will be annihilated at its maximum age $\tau$. There is an absorbing state phase transition which is controlled by this parameter. The model can demonstrate oscillatory behavior in its approach to the stationary state. These oscillations are also present in the mean-field approximation which is a first-order differential equation with time-delay. Studying dynamical critical exponents suggests that the model belongs to the DP universlity class.Comment: 4 pages, 5 figures, to be published in Phys. Rev.

Absorbing state phase transitions with quenched disorder

Quenched disorder - in the sense of the Harris criterion - is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems. In this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one-dimensional systems. The renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found. For weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder, whereas the dynamical correlations are compatible with two possible scenarios. Either they follow a power-law decay with a varying dynamical exponent, like in random quantum systems, or the dynamical correlations are logarithmically slow even for weak disorder. For models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis.Comment: 17 pages, 8 figure

Energy Transport in an Ising Disordered Model

We introduce a new microcanonical dynamics for a large class of Ising systems isolated or maintained out of equilibrium by contact with thermostats at different temperatures. Such a dynamics is very general and can be used in a wide range of situations, including disordered and topologically inhomogenous systems. Focusing on the two-dimensional ferromagnetic case, we show that the equilibrium temperature is naturally defined, and it can be consistently extended as a local temperature when far from equilibrium. This holds for homogeneous as well as for disordered systems. In particular, we will consider a system characterized by ferromagnetic random couplings $J_{ij} \in [ 1 - \epsilon, 1 + \epsilon ]$. We show that the dynamics relaxes to steady states, and that heat transport can be described on the average by means of a Fourier equation. The presence of disorder reduces the conductivity, the effect being especially appreciable for low temperatures. We finally discuss a possible singular behaviour arising for small disorder, i.e. in the limit $\epsilon \to 0$.Comment: 14 pages, 8 figure