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We present on shell-scheme for the 2PI formalism with a particular focus on the renormalized equations of motion. We first revisit the so-called Hartree approximation where we give the counterterms for both the broken and unbroken phase. Moreover, we give explicit formulas for the renormalized three- and four-point functions in the broken phase. We then turn to the sunset approximation, with only scalars and then including fermions. We give explicit formulas for the wavefunction and mass counterterms. Moreover, we show that, in particular, the two-point functions can be obtained numerically in a fast converging scheme even for large couplings of order one., Comment: 46 pages, 8 figures

We study entropy production and fluctuation relations in the restricted solid-on-solid growth model, which is a microscopic realization of the KPZ equation. Solving the one dimensional model exactly on a particular line of the phase diagram we demonstrate that entropy production quantifies the distance from equilibrium. Moreover, as an example of a physically relevant current different from the entropy, we study the symmetry of the large deviation function associated with the interface height. In a special case of a system of length L=4 we find that the probability distribution of the variation of height has a symmetric large deviation function, displaying a symmetry different from the Gallavotti-Cohen symmetry., Comment: 21 pages, 5 figures

We suggest an equal-time n-point correlation function for systems in the directed percolation universality class which is well defined in all phases and independent of initial conditions. It is defined as the probability that all points are connected with a common ancestor in the past by directed paths., Comment: LaTeX, 12 pages, 8 eps figures

We study in further detail particle models displaying a boundary-induced absorbing state phase transition [Phys. Rev. E. {\bf 65}, 046104 (2002) and Phys. Rev. Lett. {\bf 100}, 165701 (2008)] . These are one-dimensional systems consisting of a single site (the boundary) where creation and annihilation of particles occur and a bulk where particles move diffusively. We study different versions of these models, and confirm that, except for one exactly solvable bosonic variant exhibiting a discontinuous transition and trivial exponents, all the others display non-trivial behavior, with critical exponents differing from their mean-field values, representing a universality class. Finally, the relation of these systems with a $(0+1)$-dimensional non-Markovian process is discussed., Comment: 9 pages, 7 figures, minor changes

We study a simplified model for pulsed laser deposition [Phys. Rev. Lett. {\bf 87}, 135701 (2001)] by rate equations. We consider a set of equations, where islands are assumed to be point-like, as well as an improved one that takes the size of the islands into account. The first set of equations is solved exactly but its predictive power is restricted to a few pulses. The improved set of equations is integrated numerically, is in excellent agreement with simulations, and fully accounts for the crossover from continuous to pulsed deposition. Moreover, we analyze the scaling of the nucleation density and show numerical results indicating that a previously observed logarithmic scaling does not apply., Comment: 8 pages, 9 figures

We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves according to the dynamics of a contact process. As the rate for offspring production at this site is varied, the model exhibits a phase transition from a fluctuating active phase into an absorbing state. The universal properties of the transition are analyzed by numerical simulations and approximation techniques., Comment: 4 pages, 4 figures; minor changes

We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean field limit. Moreover, we introduce a graded persistence probability that a site does not flip more than n times and demonstrate how local persistence can be studied in seed simulations. Finally, the problem of spatial (as opposed to temporal) persistence is investigated., Comment: LaTeX, 24 pages, 12 figures; references added and corrected, section 4.3 rewritten

We revisit the scaling properties of a model for non-equilibrium wetting [Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the critical exponents and providing a complete scaling scheme. Moreover, we investigate a special point in the phase diagram, where the model exhibits a roughening transition related to directed percolation. We argue that in the vicinity of this point evaporation from the middle of plateaus can be interpreted as an external field in the language of directed percolation. This analogy allows us to compute the crossover exponent and to predict the form of the phase transition line close to its terminal point., Comment: 8 pages, 8 figures

We study a contact process on a two-dimensional square lattice which is diluted by randomly removing bonds with probability p. For p<1/2 and varying birth rate $\lambda$ the model was shown to exhibit a continuous phase transition which belongs to the universality class of strongly disordered directed percolation. The phase transition line terminates in a multicritical point at p=1/2 and $\lambda=\lambda*=3.55(1)$, where the model can be interpreted as a critical directed percolation process running on a critical isotropic percolation cluster. In the present work we study the multicritical point and its neighboorhood by numerical simulations, discussing possible scaling forms which could describe the critical behavior at the transition., Comment: 18 pages, 11 figures, submitted to Journal of Statistical Mechanics: Theor. Exp

A class of non-local contact processes is introduced and studied using mean-field approximation and numerical simulations. In these processes particles are created at a rate which decays algebraically with the distance from the nearest particle. It is found that the transition into the absorbing state is continuous and is characterized by continuously varying critical exponents. This model differs from the previously studied non-local directed percolation model, where particles are created by unrestricted Levy flights. It is motivated by recent studies of non-equilibrium wetting indicating that this type of non-local processes play a role in the unbinding transition. Other non-local processes which have been suggested to exist within the context of wetting are considered as well., Comment: Accepted with minor revisions by Journal of Statistical Mechanics: Theory and experiments

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 figures

In order to control aggregation phenomena in suspensions of nanoparticles, one often charges the particles electrically, e.g. by triboelectric charging. Stabilization of suspensions against aggregation of particles is an important issue, which may be realized by monopolar charging, where particles repel each other. Contrarily, bipolar charging may be used in coating processes, where smaller particles of one material coat larger particles of another material. When the two particle fractions are charged oppositely, aggregation between equally charged particles is hindered whereas aggregation between oppositely charged particles is preferred, thereby improving the coating process. We study various aspects of these two situations by theoretical investigations and computer simulations., Comment: 4 pages, 2 figures. Part of Powders & Grains 2005 proceedings

Fine powders often tend to agglomerate due to van der Waals forces between the particles. These forces can be reduced significantly by covering the particles with nanoscaled adsorbates, as shown by recent experiments. In the present work a quantitative statistical analysis of the effect of powder flow regulating nanomaterials on the adhesive forces in powders is given. Covering two spherical powder particles randomly with nanoadsorbates we compute the decrease of the mutual van der Waals force. The dependence of the force on the relative surface coverage obeys a scaling form which is independent of the used materials. The predictions by our simulations are compared to the experimental results., Comment: 18 pages, 9 figures, 1 table, LaTeX; reviewed version with minor changes, published (Powder Technology)

It is argued that some phase--transitions observed in models of non-equilibrium wetting phenomena are related to contact processes with long-range interactions. This is investigated by introducing a model where the activation rate of a site at the edge of an inactive island of length $\ell$ is $1+a\ell^{-\sigma}$. Mean--field analysis and numerical simulations indicate that for $\sigma>1$ the transition is continuous and belongs to the universality class of directed percolation, while for $0<\sigma<1$, the transition becomes first order. This criterion is then applied to discuss critical properties of various models of non--equilibrium wetting., Comment: 12 Figures. V Version resubmitted to Phys. Rev. E after referees report

We report a detailed account of the phase diagram of a recently introduced model for non-equilibrium wetting in 1+1 dimensions [Phys. Rev. Lett. 79, 2710 (1997)]. A mean field approximation is shown to reproduce the main features of the phase diagram, while providing indications for the behaviour of the wetting transition in higher dimensions. The mean field phase diagram is found to exhibit an extra transition line which does not exist in 1+1 dimensions. The line separates a phase in which the interface height distribution decays exponentially at large heights, from a superexponentially decaying phase. Implications to wetting in dimensions higher than 1+1 are discussed., Comment: RevTeX, 19 pages, 14 eps figures

The aim of this work is to understand agglomeration of charged powders suspended in nonpolar fluids. The concerted influence of electromagnetic, hydrodynamic and van der Waals forces as well as Brownian motion leads to a complex agglomeration behaviour which depends on several parameters, e.g., the ratios of electric charges, particle sizes, temperature and concentrations of the particles. Both experimental and theoretical considerations are presented.

Phase transitions from an active into an absorbing, inactive state are generically described by the critical exponents of directed percolation (DP), with upper critical dimension d_c = 4. In the framework of single-species reaction-diffusion systems, this universality class is realized by the combined processes A -> A + A, A + A -> A, and A -> \emptyset. We study a hierarchy of such DP processes for particle species A, B,..., unidirectionally coupled via the reactions A -> B, ... (with rates \mu_{AB}, ...). When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents \beta_i which are markedly reduced at each hierarchy level i >= 2. This scenario can be understood on the basis of the mean-field rate equations, which yield \beta_i = 1/2^{i-1} at the multicritical point. We then include fluctuations by using field-theoretic renormalization group techniques in d = 4-\epsilon dimensions. In the active phase, we calculate the fluctuation correction to the density exponent for the second hierarchy level, \beta_2 = 1/2 - \epsilon/8 + O(\epsilon^2). Monte Carlo simulations are then employed to determine the values for the new scaling exponents in dimensions d<= 3, including the critical initial slip exponent. Our theory is connected to certain classes of growth processes and to certain cellular automata, as well as to unidirectionally coupled pair annihilation processes. We also discuss some technical and conceptual problems of the loop expansion and their possible interpretation., Comment: 29 pages, 19 figures, revtex, 2 columns, revised Jan 1995: minor changes and additions; accepted for publication in Phys. Rev. E

Using $U_q[SU(2)]$ tensor calculus we compute the two-point scalar operators (TPSO), their averages on the ground-state give the two-point correlation functions. The TPSOs are identified as elements of the Temperley-Lieb algebra and a recurrence relation is given for them. We have not tempted to derive the analytic expressions for the correlation functions in the general case but got some partial results. For $q=e^{i \pi/3}$, all correlation functions are (trivially) zero, for $q=e^{i \pi/4}$, they are related in the continuum to the correlation functions of left-handed and right-handed Majorana fields in the half plane coupled by the boundary condition. In the case $q=e^{i \pi/6}$, one gets the correlation functions of Mittag's and Stephen's parafermions for the three-state Potts model. A diagrammatic approach to compute correlation functions is also presented., Comment: 19 pages, LaTeX, BONN-HE-93-35