811 research outputs found
Quasiperiodic Tip Splitting in Directional Solidification
We report experimental results on the tip splitting dynamics of seaweed
growth in directional solidification of succinonitrile alloys with
poly(ethylene oxide) or acetone as solutes. The seaweed or dense branching
morphology was selected by solidifying grains which are oriented close to the
{111} plane. Despite the random appearance of the growth, a quasiperiodic tip
splitting morphology was observed in which the tip alternately splits to the
left and to the right. The tip splitting frequency f was found to be related to
the growth velocity V as a power law f V^{1.5}. This finding
is consistent with the predictions of a tip splitting model that is also
presented. Small anisotropies are shown to lead to different kinds of seaweed
morphologies.Comment: 4 pages, 7 figures, submitted to Physical Review Letter
Thermodynamics of the frustrated one-dimensional spin-1/2 Heisenberg ferromagnet in a magnetic field
We calculate the low-temperature thermodynamic quantities (magnetization,
correlation functions, transverse and longitudinal correlation lengths, spin
susceptibility, and specific heat) of the frustrated one-dimensional spin-half
J1-J2 Heisenberg ferromagnet, i.e. for J2< 0.25|J1|, in an external magnetic
field using a second-order Green-function formalism and full diagonalization of
finite systems. We determine power-law relations for the field dependence of
the position and the height of the maximum of the uniform susceptibility.
Considering the specific heat at low magnetic fields, two maxima in its
temperature dependence are found.Comment: 9 pages, 9 figures, version as published in PR
Green's-function theory of the Heisenberg ferromagnet in a magnetic field
We present a second-order Green's-function theory of the one- and
two-dimensional S=1/2 ferromagnet in a magnetic field based on a decoupling of
three-spin operator products, where vertex parameters are introduced and
determined by exact relations. The transverse and longitudinal spin correlation
functions and thermodynamic properties (magnetization, isothermal magnetic
susceptibility, specific heat) are calculated self-consistently at arbitrary
temperatures and fields. In addition, exact diagonalizations on finite lattices
and, in the one-dimensional case, exact calculations by the Bethe-ansatz method
for the quantum transfer matrix are performed. A good agreement of the
Green's-function theory with the exact data, with recent quantum Monte Carlo
results, and with the spin polarization of a quantum Hall ferromagnet
is obtained. The field dependences of the position and height of the maximum in
the temperature dependence of the susceptibility are found to fit well to power
laws, which are critically analyzed in relation to the recently discussed
behavior in Landau's theory. As revealed by the spin correlation functions and
the specific heat at low fields, our theory provides an improved description of
magnetic short-range order as compared with the random phase approximation. In
one dimension and at very low fields, two maxima in the temperature dependence
of the specific heat are found. The Bethe-ansatz data for the field dependences
of the position and height of the low-temperature maximum are described by
power laws. At higher fields in one and two dimensions, the temperature of the
specific heat maximum linearly increases with the field.Comment: 9 pages, 9 figure
Influence of electron-phonon interaction on superexchange
We investigate the influence of electron-phonon coupling on the superexchange
interaction of magnetic insulators. Both the Holstein-Hubbard model where the
phonons couple to the electron density, as well as an extended Su, Schrieffer,
Heeger model where the coupling arises from modulation of the overlap integral
are studied using exact diagonalization and perturbative methods. In all cases
for both the adiabatic (but non-zero frequency) and anti-adiabatic parameter
regions the electron-phonon coupling is found to enhance the superexchange.Comment: 14 pages+4 postscript figure
Step fluctuations and random walks
The probability distribution p(l) of an atom to return to a step at distance
l from the detachment site, with a random walk in between, is exactly
enumerated. In particular, we study the dependence of p(l) on step roughness,
presence of other reflecting or absorbing steps, interaction between steps and
diffusing atom, as well as concentration of defects on the terrace neighbouring
the step. Applying Monte Carlo techniques, the time evolution of equilibrium
step fluctuations is computed for specific forms of return probabilities.
Results are compared to previous theoretical and experimental findings.Comment: 16 pages, 6 figure
Thermodynamics of layered Heisenberg magnets with arbitrary spin
We present a spin-rotation-invariant Green-function theory of long- and
short-range order in the ferro- and antiferromagnetic Heisenberg model with
arbitrary spin quantum number S on a stacked square lattice. The thermodynamic
quantities (Curie temperature T_C, N\'eel temperature T_N, specific heat C_V,
intralayer and interlayer correlation lengths) are calculated, where the
effects of the interlayer coupling and the S dependence are explored. In
addition, exact diagonalizations on finite two-dimensional (2D) lattices with
S>=1 are performed, and a very good agreement between the results of both
approaches is found. For the quasi-2D and isotropic 3D magnets, our theory
agrees well with available quantum Monte Carlo and high-temperature
series-expansion data. Comparing the quasi-2D S=1/2 magnets, we obtain the
inequalities T_N>T_C and, for small enough interlayer couplings, T_N<T_C. The
results for C_V and the intralayer correlation length are compared to
experiments on the quasi-2D antiferromagnets Zn_2VO(PO_4)_2 with S=1/2 and
La_2NiO_4 with S=1, respectively.Comment: 10 pages, 8 figures, 3 tables, submitted to Physical Review
Mean Field Theory of the Morphology Transition in Stochastic Diffusion Limited Growth
We propose a mean-field model for describing the averaged properties of a
class of stochastic diffusion-limited growth systems. We then show that this
model exhibits a morphology transition from a dense-branching structure with a
convex envelope to a dendritic one with an overall concave morphology. We have
also constructed an order parameter which describes the transition
quantitatively. The transition is shown to be continuous, which can be verified
by noting the non-existence of any hysteresis.Comment: 16 pages, 5 figure
Thermodynamics of Heisenberg ferromagnets with arbitrary spin in a magnetic field
The thermodynamic properties (magnetization, magnetic susceptibility,
transverse and longitudinal correlation lengths, specific heat) of one- and
two-dimensional ferromagnets with arbitrary spin S in a magnetic field are
investigated by a second-order Green-function theory. In addition, quantum
Monte Carlo simulations for S= 1/2 and S=1 are performed using the stochastic
series expansion method. A good agreement between the results of both
approaches is found. The field dependence of the position of the maximum in the
temperature dependence of the susceptibility fits well to a power law at low
fields and to a linear increase at high fields. The maximum height decreases
according to a power law in the whole field region. The longitudinal
correlation length may show an anomalous temperature dependence: a minimum
followed by a maximum with increasing temperature. Considering the specific
heat in one dimension and at low magnetic fields, two maxima in its temperature
dependence for both the S= 1/2 and S = 1 ferromagnets are found. For S>1 only
one maximum occurs, as in the two-dimensional ferromagnets. Relating the theory
to experiments on the S= 1/2 quasi-one-dimensional copper salt TMCuC
[(CH_3)_4NCuCl_3], a fit to the magnetization as a function of the magnetic
field yields the value of the exchange energy which is used to make predictions
for the occurrence of two maxima in the temperature dependence of the specific
heat.Comment: 17 pages, 19 figures, submitted to Phys. Rev.
Simulation of Claylike Colloids
We investigate properties of dense suspensions and sediments of small
spherical silt particles by means of a combined Molecular Dynamics (MD) and
Stochastic Rotation Dynamics (SRD) simulation. We include van der Waals and
effective electrostatic interactions between the colloidal particles, as well
as Brownian motion and hydrodynamic interactions which are calculated in the
SRD-part. We present the simulation technique and first results. We have
measured velocity distributions, diffusion coefficients, sedimentation
velocity, spatial correlation functions and we have explored the phase diagram
depending on the parameters of the potentials and on the volume fraction.Comment: 20 pages, 14 figure
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