1,865 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
Interacting Crumpled Manifolds: Exact Results to all Orders of Perturbation Theory
In this letter, we report progress on the field theory of polymerized
tethered membranes. For the toy-model of a manifold repelled by a single point,
we are able to sum the perturbation expansion in the strength g of the
interaction exactly in the limit of internal dimension D -> 2. This exact
solution is the starting point for an expansion in 2-D, which aims at
connecting to the well studied case of polymers (D=1). We here give results to
order (2-D)^4, where again all orders in g are resummed. This is a first step
towards a more complete solution of the self-avoiding manifold problem, which
might also prove valuable for polymers.Comment: 8 page
Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi model
We obtain an exact solution for the motion of a particle driven by a spring
in a Brownian random-force landscape, the Alessandro-Beatrice-Bertotti-Montorsi
(ABBM) model. Many experiments on quasi-static driving of elastic interfaces
(Barkhausen noise in magnets, earthquake statistics, shear dynamics of granular
matter) exhibit the same universal behavior as this model. It also appears as a
limit in the field theory of elastic manifolds. Here we discuss predictions of
the ABBM model for monotonous, but otherwise arbitrary, time-dependent driving.
Our main result is an explicit formula for the generating functional of
particle velocities and positions. We apply this to derive the
particle-velocity distribution following a quench in the driving velocity. We
also obtain the joint avalanche size and duration distribution and the mean
avalanche shape following a jump in the position of the confining spring. Such
non-stationary driving is easy to realize in experiments, and provides a way to
test the ABBM model beyond the stationary, quasi-static regime. We study
extensions to two elastically coupled layers, and to an elastic interface of
internal dimension d, in the Brownian force landscape. The effective action of
the field theory is equal to the action, up to 1-loop corrections obtained
exactly from a functional determinant. This provides a connection to
renormalization-group methods.Comment: 18 pages, 3 figure
Random RNA under tension
The Laessig-Wiese (LW) field theory for the freezing transition of random RNA
secondary structures is generalized to the situation of an external force. We
find a second-order phase transition at a critical applied force f = f_c. For f
f_c, the extension L as a function of
pulling force f scales as (f-f_c)^(1/gamma-1). The exponent gamma is calculated
in an epsilon-expansion: At 1-loop order gamma = epsilon/2 = 1/2, equivalent to
the disorder-free case. 2-loop results yielding gamma = 0.6 are briefly
mentioned. Using a locking argument, we speculate that this result extends to
the strong-disorder phase.Comment: 6 pages, 10 figures. v2: corrected typos, discussion on locking
argument improve
Antiferromagnetically coupled CoFeB/Ru/CoFeB trilayers
This work reports on the magnetic interlayer coupling between two amorphous
CoFeB layers, separated by a thin Ru spacer. We observe an antiferromagnetic
coupling which oscillates as a function of the Ru thickness x, with the second
antiferromagnetic maximum found for x=1.0 to 1.1 nm. We have studied the
switching of a CoFeB/Ru/CoFeB trilayer for a Ru thickness of 1.1 nm and found
that the coercivity depends on the net magnetic moment, i.e. the thickness
difference of the two CoFeB layers. The antiferromagnetic coupling is almost
independent on the annealing temperatures up to 300 degree C while an annealing
at 350 degree C reduces the coupling and increases the coercivity, indicating
the onset of crystallization. Used as a soft electrode in a magnetic tunnel
junction, a high tunneling magnetoresistance of about 50%, a well defined
plateau and a rectangular switching behavior is achieved.Comment: 3 pages, 3 figure
Interacting crumpled manifolds
In this article we study the effect of a delta-interaction on a polymerized
membrane of arbitrary internal dimension D. Depending on the dimensionality of
membrane and embedding space, different physical scenarios are observed. We
emphasize on the difference of polymers from membranes. For the latter,
non-trivial contributions appear at the 2-loop level. We also exploit a
``massive scheme'' inspired by calculations in fixed dimensions for scalar
field theories. Despite the fact that these calculations are only amenable
numerically, we found that in the limit of D to 2 each diagram can be evaluated
analytically. This property extends in fact to any order in perturbation
theory, allowing for a summation of all orders. This is a novel and quite
surprising result. Finally, an attempt to go beyond D=2 is presented.
Applications to the case of self-avoiding membranes are mentioned
In-plane deformation of a triangulated surface model with metric degrees of freedom
Using the canonical Monte Carlo simulation technique, we study a Regge
calculus model on triangulated spherical surfaces. The discrete model is
statistical mechanically defined with the variables , and , which
denote the surface position in , the metric on a two-dimensional
surface and the surface density of , respectively. The metric is
defined only by using the deficit angle of the triangles in {}. This is in
sharp contrast to the conventional Regge calculus model, where {} depends
only on the edge length of the triangles. We find that the discrete model in
this paper undergoes a phase transition between the smooth spherical phase at
and the crumpled phase at , where is the bending
rigidity. The transition is of first-order and identified with the one observed
in the conventional model without the variables and . This implies
that the shape transformation transition is not influenced by the metric
degrees of freedom. It is also found that the model undergoes a continuous
transition of in-plane deformation. This continuous transition is reflected in
almost discontinuous changes of the surface area of and that of ,
where the surface area of is conjugate to the density variable .Comment: 13 pages, 7 figure
Loop Model with Generalized Fugacity in Three Dimensions
A statistical model of loops on the three-dimensional lattice is proposed and
is investigated. It is O(n)-type but has loop fugacity that depends on global
three-dimensional shapes of loops in a particular fashion. It is shown that,
despite this non-locality and the dimensionality, a layer-to-layer transfer
matrix can be constructed as a product of local vertex weights for infinitely
many points in the parameter space. Using this transfer matrix, the site
entropy is estimated numerically in the fully packed limit.Comment: 16pages, 4 eps figures, (v2) typos and Table 3 corrected. Refs added,
(v3) an error in an explanation of fig.2 corrected. Refs added. (v4) Changes
in the presentatio
Shock statistics in higher-dimensional Burgers turbulence
We conjecture the exact shock statistics in the inviscid decaying Burgers
equation in D>1 dimensions, with a special class of correlated initial
velocities, which reduce to Brownian for D=1. The prediction is based on a
field-theory argument, and receives support from our numerical calculations. We
find that, along any given direction, shocks sizes and locations are
uncorrelated.Comment: 4 pages, 8 figure
Phase transitions of a tethered surface model with a deficit angle term
Nambu-Goto model is investigated by using the canonical Monte Carlo
simulations on fixed connectivity surfaces of spherical topology. Three
distinct phases are found: crumpled, tubular, and smooth. The crumpled and the
tubular phases are smoothly connected, and the tubular and the smooth phases
are connected by a discontinuous transition. The surface in the tubular phase
forms an oblong and one-dimensional object similar to a one-dimensional linear
subspace in the Euclidean three-dimensional space R^3. This indicates that the
rotational symmetry inherent in the model is spontaneously broken in the
tubular phase, and it is restored in the smooth and the crumpled phases.Comment: 6 pages with 6 figure
- …