Tricritical directed percolation

We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The incorporated higher-order reaction terms lead to a non-trivial phase diagram. In particular, a line of continuous phase transitions is separated by a tricritical point from a line of discontinuous phase transitions. The corresponding tricritical scaling behavior is analyzed in detail, i.e., we determine the critical exponents, various universal scaling functions as well as universal amplitude combinations

Finite-size scaling of directed percolation above the upper critical dimension

We consider analytically as well as numerically the finite-size scaling behavior in the stationary state near the non-equilibrium phase transition of directed percolation within the mean field regime, i.e., above the upper critical dimension. Analogous to equilibrium, usual finite-size scaling is valid below the upper critical dimension, whereas it fails above. Performing a momentum analysis of associated path integrals we derive modified finite-size scaling forms of the order parameter and its higher moments. The results are confirmed by numerical simulations of corresponding high-dimensional lattice models.Comment: 4 pages, one figur

Universal scaling behavior at the upper critical dimension of non-equilibrium continuous phase transitions

In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of the upper critical dimension. We apply our method to a non-equilibrium continuous phase transition. But focusing on the equation of state of the phase transition it is easy to extend our analysis to all equilibrium and non-equilibrium phase transitions observed numerically or experimentally.Comment: 4 pages, 3 figure

Scaling of waves in the Bak-Tang-Wiesenfeld sandpile model

We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk and boundary waves by means of their correspondence to spanning trees, and by extensive numerical simulations. While the scaling behavior of avalanches is complex and usually not governed by simple scaling laws, we show that the probability distributions for waves display clear power law asymptotic behavior in perfect agreement with the analytical predictions. Critical exponents are obtained for the distributions of radius, area, and duration, of bulk and boundary waves. Relations between them and fractal dimensions of waves are derived. We confirm that the upper critical dimension D_u of the model is 4, and calculate logarithmic corrections to the scaling behavior of waves in D=4. In addition we present analytical estimates for bulk avalanches in dimensions D>=4 and simulation data for avalanches in D<=3. For D=2 they seem not easy to interpret.Comment: 12 pages, 17 figures, submitted to Phys. Rev.

The Chromo-Dielectric Soliton Model: Quark Self Energy and Hadron Bags

The chromo-dielectric soliton model (CDM) is Lorentz- and chirally-invariant. It has been demonstrated to exhibit dynamical chiral symmetry breaking and spatial confinement in the locally uniform approximation. We here study the full nonlocal quark self energy in a color-dielectric medium modeled by a two parameter Fermi function. Here color confinement is manifest. The self energy thus obtained is used to calculate quark wave functions in the medium which, in turn, are used to calculate the nucleon and pion masses in the one gluon exchange approximation. The nucleon mass is fixed to its empirical value using scaling arguments; the pion mass (for massless current quarks) turns out to be small but non-zero, depending on the model parameters.Comment: 24 pages, figures available from the author

Universality in sandpiles

We perform extensive numerical simulations of different versions of the sandpile model. We find that previous claims about universality classes are unfounded, since the method previously employed to analyze the data suffered a systematic bias. We identify the correct scaling behavior and conclude that sandpiles with stochastic and deterministic toppling rules belong to the same universality class.Comment: 4 pages, 4 ps figures; submitted to Phys. Rev.

The depinning transition of a driven interface in the random-field Ising model around the upper critical dimension

We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal fluctuations. Although thermal fluctuations drive the system away from criticality the order parameter obeys a certain scaling law for sufficiently low temperatures and the corresponding exponents are determined. Our results suggest that the so-called upper critical dimension of the depinning transition is five and that the systems belongs to the universality class of the quenched Edward-Wilkinson equation.Comment: accepted for publication in Phys. Rev.

Traffic jams and ordering far from thermal equilibrium

The recently suggested correspondence between domain dynamics of traffic models and the asymmetric chipping model is reviewed. It is observed that in many cases traffic domains perform the two characteristic dynamical processes of the chipping model, namely chipping and diffusion. This correspondence indicates that jamming in traffic models in which all dynamical rates are non-deterministic takes place as a broad crossover phenomenon, rather than a sharp transition. Two traffic models are studied in detail and analyzed within this picture.Comment: Contribution to the Niels Bohr Summer Institute on Complexity and Criticality; to appear in a Per Bak Memorial Issue of PHYSICA

Driving, conservation and absorbing states in sandpiles

We use a phenomenological field theory, reflecting the symmetries and conservation laws of sandpiles, to compare the driven dissipative sandpile, widely studied in the context of self-organized criticality, with the corresponding fixed-energy model. The latter displays an absorbing-state phase transition with upper critical dimension $d_c=4$. We show that the driven model exhibits a fundamentally different approach to the critical point, and compute a subset of critical exponents. We present numerical simulations in support of our theoretical predictions.Comment: 12 pages, 2 figures; revised version with substantial changes and improvement

Finite-size scaling of directed percolation in the steady state

Recently, considerable progress has been made in understanding finite-size scaling in equilibrium systems. Here, we study finite-size scaling in non-equilibrium systems at the instance of directed percolation (DP), which has become the paradigm of non-equilibrium phase transitions into absorbing states, above, at and below the upper critical dimension. We investigate the finite-size scaling behavior of DP analytically and numerically by considering its steady state generated by a homogeneous constant external source on a d-dimensional hypercube of finite edge length L with periodic boundary conditions near the bulk critical point. In particular, we study the order parameter and its higher moments using renormalized field theory. We derive finite-size scaling forms of the moments in a one-loop calculation. Moreover, we introduce and calculate a ratio of the order parameter moments that plays a similar role in the analysis of finite size scaling in absorbing nonequilibrium processes as the famous Binder cumulant in equilibrium systems and that, in particular, provides a new signature of the DP universality class. To complement our analytical work, we perform Monte Carlo simulations which confirm our analytical results.Comment: 21 pages, 6 figure