16,023 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

### The Resistance of Feynman Diagrams and the Percolation Backbone Dimension

We present a new view of Feynman diagrams for the field theory of transport
on percolation clusters. The diagrams for random resistor networks are
interpreted as being resistor networks themselves. This simplifies the field
theory considerably as we demonstrate by calculating the fractal dimension
$D_B$ of the percolation backbone to three loop order. Using renormalization
group methods we obtain $D_B = 2 + \epsilon /21 - 172\epsilon^2 /9261 + 2
\epsilon^3 (- 74639 + 22680 \zeta (3))/4084101$, where $\epsilon = 6-d$ with
$d$ being the spatial dimension and $\zeta (3) = 1.202057..$.Comment: 10 pages, 2 figure

### 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 ($\theta$-)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
$\theta^\prime$-transition could be a fluctuation induced first order
transition.Comment: 4 page

### Levy-flight spreading of epidemic processes leading to percolating clusters

We consider two stochastic processes, the Gribov process and the general
epidemic process, that describe the spreading of an infectious disease. In
contrast to the usually assumed case of short-range infections that lead, at
the critical point, to directed and isotropic percolation respectively, we
consider long-range infections with a probability distribution decaying in d
dimensions with the distance as 1/R^{d+\sigma}. By means of Wilson's momentum
shell renormalization-group recursion relations, the critical exponents
characterizing the growing fractal clusters are calculated to first order in an
\epsilon-expansion. It is shown that the long-range critical behavior changes
continuously to its short-range counterpart for a decay exponent of the
infection \sigma =\sigma_c>2.Comment: 9 pages ReVTeX, 2 postscript figures included, submitted to Eur.
Phys. J.

### Group corings

We introduce group corings, and study functors between categories of
comodules over group corings, and the relationship to graded modules over
graded rings. Galois group corings are defined, and a Structure Theorem for the
$G$-comodules over a Galois group coring is given. We study (graded) Morita
contexts associated to a group coring. Our theory is applied to group corings
associated to a comodule algebra over a Hopf group coalgebra.Comment: 38 page

### 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 $\epsilon$-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

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