16,062 research outputs found
Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem
We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise
correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho
and the spatial dimension d. By means of a stochastic Cole-Hopf transformation,
the critical and correction-to-scaling exponents at the roughening transition
are determined to all orders in a (d - d_c) expansion. We also argue that there
is a intriguing possibility that the rough phases above and below the lower
critical dimension d_c = 2 (1 + \rho) are genuinely different which could lead
to a re-interpretation of results in the literature.Comment: Latex, 7 pages, eps files for two figures as well as Europhys. Lett.
style files included; slightly expanded reincarnatio
Drived diffusion of vector fields
A model for the diffusion of vector fields driven by external forces is
proposed. Using the renormalization group and the -expansion, the
dynamical critical properties of the model with gaussian noise for dimensions
below the critical dimension are investigated and new transport universality
classes are obtained.Comment: 11 pages, title changed, anisotropic diffusion further discussed and
emphasize
Microscopic Non-Universality versus Macroscopic Universality in Algorithms for Critical Dynamics
We study relaxation processes in spin systems near criticality after a quench
from a high-temperature initial state. Special attention is paid to the stage
where universal behavior, with increasing order parameter emerges from an early
non-universal period. We compare various algorithms, lattice types, and
updating schemes and find in each case the same universal behavior at
macroscopic times, despite of surprising differences during the early
non-universal stages.Comment: 9 pages, 3 figures, RevTeX, submitted to Phys. Rev. Let
Spontaneous Symmetry Breaking in Directed Percolation with Many Colors: Differentiation of Species in the Gribov Process
A general field theoretic model of directed percolation with many colors that
is equivalent to a population model (Gribov process) with many species near
their extinction thresholds is presented. It is shown that the multicritical
behavior is always described by the well known exponents of Reggeon field
theory. In addition this universal model shows an instability that leads in
general to a total asymmetry between each pair of species of a cooperative
society.Comment: 4 pages, 2 Postscript figures, uses multicol.sty, submitte
Fresh look at randomly branched polymers
We develop a new, dynamical field theory of isotropic randomly branched
polymers, and we use this model in conjunction with the renormalization group
(RG) to study several prominent problems in the physics of these polymers. Our
model provides an alternative vantage point to understand the swollen phase via
dimensional reduction. We reveal a hidden Becchi-Rouet-Stora (BRS) symmetry of
the model that describes the collapse (-)transition to compact
polymer-conformations, and calculate the critical exponents to 2-loop order. It
turns out that the long-standing 1-loop results for these exponents are not
entirely correct. A runaway of the RG flow indicates that the so-called
-transition could be a fluctuation induced first order
transition.Comment: 4 page
On Critical Exponents and the Renormalization of the Coupling Constant in Growth Models with Surface Diffusion
It is shown by the method of renormalized field theory that in contrast to a
statement based on a mathematically ill-defined invariance transformation and
found in most of the recent publications on growth models with surface
diffusion, the coupling constant of these models renormalizes nontrivially.
This implies that the widely accepted supposedly exact scaling exponents are to
be corrected. A two-loop calculation shows that the corrections are small and
these exponents seem to be very good approximations.Comment: 4 pages, revtex, 2 postscript figures, to appear in Phys.Rev.Let
Renormalized field theory and particle density profile in driven diffusive systems with open boundaries
We investigate the density profile in a driven diffusive system caused by a
plane particle source perpendicular to the driving force. Focussing on the case
of critical bulk density we use a field theoretic renormalization
group approach to calculate the density as a function of the distance
from the particle source at first order in (: spatial
dimension). For we find reasonable agreement with the exact solution
recently obtained for the asymmetric exclusion model. Logarithmic corrections
to the mean field profile are computed for with the result for .Comment: 32 pages, RevTex, 4 Postscript figures, to appear in Phys. Rev.
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.
Differential thermal analysis and solution growth of intermetallic compounds
To obtain single crystals by solution growth, an exposed primary
solidification surface in the appropriate, but often unknown, equilibrium alloy
phase diagram is required. Furthermore, an appropriate crucible material is
needed, necessary to hold the molten alloy during growth, without being
attacked by it. Recently, we have used the comparison of realistic simulations
with experimental differential thermal analysis (DTA) curves to address both
these problems. We have found: 1) complex DTA curves can be interpreted to
determine an appropriate heat treatment and starting composition for solution
growth, without having to determine the underlying phase diagrams in detail. 2)
DTA can facilitate identification of appropriate crucible materials. DTA can
thus be used to make the procedure to obtain single crystals of a desired phase
by solution growth more efficient. We will use some of the systems for which we
have recently obtained single-crystalline samples using the combination of DTA
and solution growth as examples. These systems are TbAl, PrNiSi,
and YMnAl.Comment: 17 pages, 8 figure
Transport on Directed Percolation Clusters
We study random lattice networks consisting of resistor like and diode like
bonds. For investigating the transport properties of these random resistor
diode networks we introduce a field theoretic Hamiltonian amenable to
renormalization group analysis. We focus on the average two-port resistance at
the transition from the nonpercolating to the directed percolating phase and
calculate the corresponding resistance exponent to two-loop order.
Moreover, we determine the backbone dimension of directed percolation
clusters to two-loop order. We obtain a scaling relation for that is in
agreement with well known scaling arguments.Comment: 4 page
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