Mean-field scaling function of the universality class of absorbing phase transitions with a conserved field

We consider two mean-field like models which belong to the universality class of absorbing phase transitions with a conserved field. In both cases we derive analytically the order parameter as function of the control parameter and of an external field conjugated to the order parameter. This allows us to calculate the universal scaling function of the mean-field behavior. The obtained universal function is in perfect agreement with recently obtained numerical data of the corresponding five and six dimensional models, showing that four is the upper critical dimension of this particular universality class.Comment: 8 pages, 2 figures, accepted for publication in J. Phys.

Moment analysis of the probability distributions of different sandpile models

We reconsider the moment analysis of the Bak-Tang-Wiesenfeld and the Manna sandpile model in two and three dimensions. In contrast to recently performed investigations our analysis turns out that the models are characterized by different scaling behavior, i.e., they belong to different universality classes.Comment: 6 pages, 6 figures, accepted for publication in Physical Review

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

Nonequilibrium critical behavior of a species coexistence model

A biologically motivated model for spatio-temporal coexistence of two competing species is studied by mean-field theory and numerical simulations. In d>1 dimensions the phase diagram displays an extended region where both species coexist, bounded by two second-order phase transition lines belonging to the directed percolation universality class. The two transition lines meet in a multicritical point, where a non-trivial critical behavior is observed.Comment: 11 page

Absorbing boundaries in the conserved Manna model

The conserved Manna model with a planar absorbing boundary is studied in various space dimensions. We present a heuristic argument that allows one to compute the surface critical exponent in one dimension analytically. Moreover, we discuss the mean field limit that is expected to be valid in d>4 space dimensions and demonstrate how the corresponding partial differential equations can be solved.Comment: 8 pages, 4 figures; v1 was changed by replacing the co-authors name "L\"ubeck" with "Lubeck" (metadata only

Rank 3 permutation characters and maximal subgroups

In this paper we classify all maximal subgroups M of a nearly simple primitive rank 3 group G of type L=Omega_{2m+1}(3), m > 3; acting on an L-orbit E of non-singular points of the natural module for L such that 1_P^G <=1_M^G where P is a stabilizer of a point in E. This result has an application to the study of minimal genera of algebraic curves which admit group actions.Comment: 41 pages, to appear in Forum Mathematicu

Crossovers from parity conserving to directed percolation universality

The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method. In case of models exhibiting Z_2 symmetric absorbing phases (the NEKIMCA and Grassberger's A stochastic cellular automaton) the introduction of an external symmetry breaking field causes a crossover to kink parity conserving models characterized by dynamical scaling of the directed percolation (DP) and the crossover exponent: 1/\phi ~ 0.53(2). In case an even offspringed branching and annihilating random walk model (dual to NEKIMCA) the introduction of spontaneous particle decay destroys the parity conservation and results in a crossover to the DP class characterized by the crossover exponent: 1/\phi\simeq 0.205(5). The two different kinds of crossover operators can't be mapped onto each other and the resulting models show a diversity within the DP universality class in one dimension. These 'sub-classes' differ in cluster scaling exponents.Comment: 6 pages, 6 figures, accepted version in PR

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.

Critical behavior of a traffic flow model

The Nagel-Schreckenberg traffic flow model shows a transition from a free flow regime to a jammed regime for increasing car density. The measurement of the dynamical structure factor offers the chance to observe the evolution of jams without the necessity to define a car to be jammed or not. Above the jamming transition the dynamical structure factor exhibits for a given k-value two maxima corresponding to the separation of the system into the free flow phase and jammed phase. We obtain from a finite-size scaling analysis of the smallest jam mode that approaching the transition long range correlations of the jams occur.Comment: 5 pages, 7 figures, accepted for publication in Physical Review

Fluctuations and correlations in sandpile models

We perform numerical simulations of the sandpile model for non-vanishing driving fields $h$ and dissipation rates $\epsilon$. Unlike simulations performed in the slow driving limit, the unique time scale present in our system allows us to measure unambiguously response and correlation functions. We discuss the dynamic scaling of the model and show that fluctuation-dissipation relations are not obeyed in this system.Comment: 5 pages, latex, 4 postscript figure