481 research outputs found
Violation of the Widom scaling law for effective crossover exponents
In this work we consider the universal crossover behavior of two
non-equilibrium systems exhibiting a continuous phase transition. Focusing on
the field driven crossover from mean-field to non-mean-field scaling behavior
we show that the well-known Widom scaling law is violated for the effective
exponents in the so-called crossover regime.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev.
Continuously varying exponents in a sandpile model with dissipation near surface
We consider the directed Abelian sandpile model in the presence of sink sites
whose density f_t at depth t below the top surface varies as c~1/t^chi. For
chi>1 the disorder is irrelevant. For chi<1, it is relevant and the model is no
longer critical for any nonzero c. For chi=1 the exponents of the avalanche
distributions depend continuously on the amplitude c of the disorder. We
calculate this dependence exactly, and verify the results with simulations.Comment: 13 pages, 4 figures, accepted for publication in J. Stat. Phy
Universal scaling behavior of directed percolation around the upper critical dimension
In this work we consider the steady state scaling behavior of directed
percolation around the upper critical dimension. In particular we determine
numerically the order parameter, its fluctuations as well as the susceptibility
as a function of the control parameter and the conjugated field. Additionally
to the universal scaling functions, several universal amplitude combinations
are considered. We compare our results with those of a renormalization group
approach.Comment: 19 pages, 8 figures, accepted for publication in J. Stat. Phy
A deterministic sandpile automaton revisited
The Bak-Tang-Wiesenfeld (BTW) sandpile model is a cellular automaton which
has been intensively studied during the last years as a paradigm for
self-organized criticality. In this paper, we reconsider a deterministic
version of the BTW model introduced by Wiesenfeld, Theiler and McNamara, where
sand grains are added always to one fixed site on the square lattice. Using the
Abelian sandpile formalism we discuss the static properties of the system. We
present numerical evidence that the deterministic model is only in the BTW
universality class if the initial conditions and the geometric form of the
boundaries do not respect the full symmetry of the square lattice.Comment: 7 pages, 8 figures, EPJ style, accepted for publication in European
Physical Journal
Density fluctuations and phase separation in a traffic flow model
Within the Nagel-Schreckenberg traffic flow model we consider the transition
from the free flow regime to the jammed regime. We introduce a method of
analyzing the data which is based on the local density distribution. This
analyzes allows us to determine the phase diagram and to examine the separation
of the system into a coexisting free flow phase and a jammed phase above the
transition. The investigation of the steady state structure factor yields that
the decomposition in this phase coexistence regime is driven by density
fluctuations, provided they exceed a critical wavelength.Comment: in 'Traffic and Granular Flow 97', edited by D.E. Wolf and M.
Schreckenberg, Springer, Singapore (1998
Interface Motion in Disordered Ferromagnets
We consider numerically the depinning transition in the random-field Ising
model. Our analysis reveals that the three and four dimensional model displays
a simple scaling behavior whereas the five dimensional scaling behavior is
affected by logarithmic corrections. This suggests that d=5 is the upper
critical dimension of the depinning transition in the random-field Ising model.
Furthermore, we investigate the so-called creep regime (small driving fields
and temperatures) where the interface velocity is given by an Arrhenius law.Comment: some misprints correcte
Cluster mean-field study of the parity conserving phase transition
The phase transition of the even offspringed branching and annihilating
random walk is studied by N-cluster mean-field approximations on
one-dimensional lattices. By allowing to reach zero branching rate a phase
transition can be seen for any N <= 12.The coherent anomaly extrapolations
applied for the series of approximations results in and
.Comment: 6 pages, 5 figures, 1 table included, Minor changes, scheduled for
pubication in PR
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