191 research outputs found
Microscopic mechanism for the 1/8 magnetization plateau in SrCu_2(BO_3)_2
The frustrated quantum magnet SrCu_2(BO_3)_2 shows a remarkably rich phase
diagram in an external magnetic field including a sequence of magnetization
plateaux. The by far experimentally most studied and most prominent
magnetization plateau is the 1/8 plateau. Theoretically, one expects that this
material is well described by the Shastry-Sutherland model. But recent
microscopic calculations indicate that the 1/8 plateau is energetically not
favored. Here we report on a very simple microscopic mechanism which naturally
leads to a 1/8 plateau for realistic values of the magnetic exchange constants.
We show that the 1/8 plateau with a diamond unit cell benefits most compared to
other plateau structures from quantum fluctuations which to a large part are
induced by Dzyaloshinskii-Moriya interactions. Physically, such couplings
result in kinetic terms in an effective hardcore boson description leading to a
renormalization of the energy of the different plateaux structures which we
treat in this work on the mean-field level. The stability of the resulting
plateaux are discussed. Furthermore, our results indicate a series of stripe
structures above 1/8 and a stable magnetization plateau at 1/6. Most
qualitative aspects of our microscopic theory agree well with a recently
formulated phenomenological theory for the experimental data of SrCu_2(BO_3)_2.
Interestingly, our calculations point to a rather large ratio of the magnetic
couplings in the Shastry-Sutherland model such that non-perturbative effects
become essential for the understanding of the frustrated quantum magnet
SrCu_2(BO_3)_2.Comment: 24 pages, 24 figure
An alternative field theory for the Kosterlitz-Thouless transition
We extend a Gaussian model for the internal electrical potential of a
two-dimensional Coulomb gas by a non-Gaussian measure term, which singles out
the physically relevant configurations of the potential. The resulting
Hamiltonian, expressed as a functional of the internal potential, has a
surprising large-scale limit: The additional term simply counts the number of
maxima and minima of the potential. The model allows for a transparent
derivation of the divergence of the correlation length upon lowering the
temperature down to the Kosterlitz-Thouless transition point.Comment: final version, extended discussion, appendix added, 8 pages, no
figure, uses IOP documentclass iopar
Distributions of absolute central moments for random walk surfaces
We study periodic Brownian paths, wrapped around the surface of a cylinder.
One characteristic of such a path is its width square, , defined as its
variance. Though the average of over all possible paths is well known,
its full distribution function was investigated only recently. Generalising
to , defined as the -th power of the {\it magnitude} of the
deviations of the path from its mean, we show that the distribution functions
of these also scale and obtain the asymptotic behaviour for both large and
small
Magnetization of SrCu2(BO3)2 in ultrahigh magnetic fields up to 118 T
The magnetization process of the orthogonal-dimer antiferromagnet SrCu2(BO3)2
is investigated in high magnetic fields of up to 118 T. A 1/2 plateau is
clearly observed in the field range 84 to 108 T in addition to 1/8, 1/4 and 1/3
plateaux at lower fields. Using a combination of state-of-the-art numerical
simulations, the main features of the high-field magnetization, a 1/2 plateau
of width 24 T, a 1/3 plateau of width 34 T, and no 2/5 plateau, are shown to
agree quantitatively with the Shastry-Sutherland model if the ratio of inter-
to intra-dimer exchange interactions J'/J=0.63. It is further predicted that
the intermediate phase between the 1/3 and 1/2 plateau is not uniform but
consists of a 1/3 supersolid followed by a 2/5 supersolid and possibly a
domain-wall phase, with a reentrance into the 1/3 supersolid above the 1/2
plateau.Comment: 5 pages + 10 pages supplemental materia
Integrated environmental risk assessment of major accidents in the transport of hazardous substances
At present, the environmental risk assessment of major accidents is mainly carried out for stationary risk sources. Only marginal attention is paid to mobile risk sources, while the currently available methodologies require a relevant expertise and time for their application, which is only partially possible in most scenarios. In the present study, an integrated approach to environmental risk assessment in the transport of hazardous substances (iTRANSRISK) was developed. The approach proposed is based on the principle of index-based assessment of leakage scenarios involving toxic and flammable substances during transport, in the context of indexing environmental vulnerability. The key point of the method is the conversion of local-specific data concerning the risk potential of the transported substance, the consequences and the probability of a major accident, and environmental vulnerability assessment into a single entity. The created integral approach is proposed for the needs of carriers of the hazardous substances and the state administration bodies. The proposed approach is determined for the screening risk assessment at the beginning of the process of the planning a suitable transport routes and the results are for information only. An example of the application of the iTRANSRISK integrated approach is demonstrated considering an explosion scenario following a propane tanker leak (18 t) in a forested area, with moderately susceptible soils and no surface water or groundwater affected
Signed zeros of Gaussian vector fields-density, correlation functions and curvature
We calculate correlation functions of the (signed) density of zeros of
Gaussian distributed vector fields. We are able to express correlation
functions of arbitrary order through the curvature tensor of a certain abstract
Riemann-Cartan or Riemannian manifold. As an application, we discuss one- and
two-point functions. The zeros of a two-dimensional Gaussian vector field model
the distribution of topological defects in the high-temperature phase of
two-dimensional systems with orientational degrees of freedom, such as
superfluid films, thin superconductors and liquid crystals.Comment: 14 pages, 1 figure, uses iopart.cls, improved presentation, to appear
in J. Phys.
Dynamic Scaling of Width Distribution in Edwards--Wilkinson Type Models of Interface Dynamics
Edwards--Wilkinson type models are studied in 1+1 dimensions and the
time-dependent distribution, P_L(w^2,t), of the square of the width of an
interface, w^2, is calculated for systems of size L. We find that, using a flat
interface as an initial condition, P_L(w^2,t) can be calculated exactly and it
obeys scaling in the form _\infty P_L(w^2,t) = Phi(w^2 / _\infty,
t/L^2) where _\infty is the stationary value of w^2. For more complicated
initial states, scaling is observed only in the large- time limit and the
scaling function depends on the initial amplitude of the longest wavelength
mode. The short-time limit is also interesting since P_L(w^2,t) is found to
closely approximate the log-normal distribution. These results are confirmed by
Monte Carlo simulations on a `roof-top' model of surface evolution.Comment: 5 pages, latex, 3 ps figures in a separate files, submitted to
Phys.Rev.
On the Nodal Count Statistics for Separable Systems in any Dimension
We consider the statistics of the number of nodal domains aka nodal counts
for eigenfunctions of separable wave equations in arbitrary dimension. We give
an explicit expression for the limiting distribution of normalised nodal counts
and analyse some of its universal properties. Our results are illustrated by
detailed discussion of simple examples and numerical nodal count distributions.Comment: 21 pages, 4 figure
The distribution of extremal points of Gaussian scalar fields
We consider the signed density of the extremal points of (two-dimensional)
scalar fields with a Gaussian distribution. We assign a positive unit charge to
the maxima and minima of the function and a negative one to its saddles. At
first, we compute the average density for a field in half-space with Dirichlet
boundary conditions. Then we calculate the charge-charge correlation function
(without boundary). We apply the general results to random waves and random
surfaces. Furthermore, we find a generating functional for the two-point
function. Its Legendre transform is the integral over the scalar curvature of a
4-dimensional Riemannian manifold.Comment: 22 pages, 8 figures, corrected published versio
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