216 research outputs found
Screening of charged singularities of random fields
Many types of point singularity have a topological index, or 'charge',
associated with them. For example the phase of a complex field depending on two
variables can either increase or decrease on making a clockwise circuit around
a simple zero, enabling the zeros to be assigned charges of plus or minus one.
In random fields we can define a correlation function for the charge-weighted
density of singularities. In many types of random fields, this correlation
function satisfies an identity which shows that the singularities 'screen' each
other perfectly: a positive singularity is surrounded by an excess of
concentration of negatives which exactly cancel its charge, and vice-versa.
This paper gives a simple and widely applicable derivation of this result. A
counterexample where screening is incomplete is also exhibited.Comment: 12 pages, no figures. Minor revision of manuscript submitted to J.
Phys. A, August 200
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
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
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
Random wave functions and percolation
Recently it was conjectured that nodal domains of random wave functions are
adequately described by critical percolation theory. In this paper we
strengthen this conjecture in two respects. First, we show that, though wave
function correlations decay slowly, a careful use of Harris' criterion confirms
that these correlations are unessential and nodal domains of random wave
functions belong to the same universality class as non critical percolation.
Second, we argue that level domains of random wave functions are described by
the non-critical percolation model.Comment: 13 page
Critical holes in undercooled wetting layers
The profile of a critical hole in an undercooled wetting layer is determined
by the saddle-point equation of a standard interface Hamiltonian supported by
convenient boundary conditions. It is shown that this saddle-point equation can
be mapped onto an autonomous dynamical system in a three-dimensional phase
space. The corresponding flux has a polynomial form and in general displays
four fixed points, each with different stability properties. On the basis of
this picture we derive the thermodynamic behaviour of critical holes in three
different nucleation regimes of the phase diagram.Comment: 18 pages, LaTeX, 6 figures Postscript, submitted to J. Phys.
The Statistics of the Points Where Nodal Lines Intersect a Reference Curve
We study the intersection points of a fixed planar curve with the
nodal set of a translationally invariant and isotropic Gaussian random field
\Psi(\bi{r}) and the zeros of its normal derivative across the curve. The
intersection points form a discrete random process which is the object of this
study. The field probability distribution function is completely specified by
the correlation G(|\bi{r}-\bi{r}'|) = .
Given an arbitrary G(|\bi{r}-\bi{r}'|), we compute the two point
correlation function of the point process on the line, and derive other
statistical measures (repulsion, rigidity) which characterize the short and
long range correlations of the intersection points. We use these statistical
measures to quantitatively characterize the complex patterns displayed by
various kinds of nodal networks. We apply these statistics in particular to
nodal patterns of random waves and of eigenfunctions of chaotic billiards. Of
special interest is the observation that for monochromatic random waves, the
number variance of the intersections with long straight segments grows like , as opposed to the linear growth predicted by the percolation model,
which was successfully used to predict other long range nodal properties of
that field.Comment: 33 pages, 13 figures, 1 tabl
Geometric characterization of nodal domains: the area-to-perimeter ratio
In an attempt to characterize the distribution of forms and shapes of nodal
domains in wave functions, we define a geometric parameter - the ratio
between the area of a domain and its perimeter, measured in units of the
wavelength . We show that the distribution function can
distinguish between domains in which the classical dynamics is regular or
chaotic. For separable surfaces, we compute the limiting distribution, and show
that it is supported by an interval, which is independent of the properties of
the surface. In systems which are chaotic, or in random-waves, the
area-to-perimeter distribution has substantially different features which we
study numerically. We compare the features of the distribution for chaotic wave
functions with the predictions of the percolation model to find agreement, but
only for nodal domains which are big with respect to the wavelength scale. This
work is also closely related to, and provides a new point of view on
isoperimetric inequalities.Comment: 22 pages, 11 figure
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