15,719 research outputs found
Frustrated Blume-Emery-Griffiths model
A generalised integer S Ising spin glass model is analysed using the replica
formalism. The bilinear couplings are assumed to have a Gaussian distribution
with ferromagnetic mean = Jo. Incorporation of a quadrupolar interaction
term and a chemical potential leads to a richer phase diagram with transitions
of first and second order. The first order transition may be interpreted as a
phase separation, and contrary to what has been argued previously, it persists
in the presence of disorder. Finally, the stability of the replica symmetric
solution with respect to fluctuations in replica space is analysed, and the
transition lines are obtained both analytically and numerically.Comment: 16 pages, 11 figure
Improved variational description of the Wick-Cutkosky model with the most general quadratic trial action
We generalize the worldline variational approach to field theory by
introducing a trial action which allows for anisotropic terms to be induced by
external 4-momenta of Green's functions. By solving the ensuing variational
equations numerically we demonstrate that within the (quenched) scalar
Wick-Cutkosky model considerable improvement can be achieved over results
obtained previously with isotropic actions. In particular, the critical
coupling associated with the instability of the model is lowered, in accordance
with expectations from Baym's proof of the instability in the unquenched
theory. The physical picture associated with a different quantum mechanical
motion of the dressed particle along and perpendicular to its classical
momentum is discussed. Indeed, we find that for large couplings the dressed
particle is strongly distorted in the direction of its four-momentum. In
addition, we obtain an exact relation between the renormalized coupling of the
theory and the propagator. Along the way we introduce new and efficient methods
to evaluate the averages needed in the variational approach and apply them to
the calculation of the 2-point function.Comment: 32 pages, 4 figures, Latex. Some typos corrected and expanded
discussion of the instability of the model provided. Accepted in Eur. Phys.
J.
The dwarf nova SS Cygni: what is wrong?
Since the Fine Guiding Sensor (FGS) on the Hubble Space Telescope (HST) was
used to measure the distance to SS Cyg to be pc, it became apparent
that at this distance the disc instability model fails to explain the absolute
magnitude during outburst. It remained, however, an open question whether the
model or the distance have to be revised. Recent observations led to a revision
of the system parameters of SS Cyg and seem to be consistent with a distance of
d\gta 140 pc. We re-discuss the problem taking into account the new binary
and stellar parameters measured for SS Cyg. We confront not only the
observations with the predictions of the disc instability model but also
compare SS Cyg with other dwarf novae and nova-like systems. We assume the disc
during outburst to be in a quasi stationary state and use the black-body
approximation to estimate the accretion rate during outburst as a function of
distance. Using published analysis of the long term light curve we determine
the mean mass transfer rate of SS Cyg as a function of distance and compare the
result with mass transfer rates derived for other dwarf novae and nova-like
systems. At a distance of d\gta 140 pc, both the accretion rate during
outburst as well as the mean mass transfer rate of SS Cyg contradict the disc
instability model. More important, at such distances we find the mean mass
transfer rate of SS Cyg to be higher or comparable to those derived for
nova-like systems. Our findings show that a distance to SS Cyg \gta 140 pc
contradicts the main concepts developed for accretion discs in cataclysmic
variables during the last 30 years. Either our current picture of disc
accretion in these systems must be revised or the distance to SS Cyg is pcComment: 6 pages, 3 figures, accepted for publication in Astronomy and
Astrophysic
Cut Size Statistics of Graph Bisection Heuristics
We investigate the statistical properties of cut sizes generated by heuristic
algorithms which solve approximately the graph bisection problem. On an
ensemble of sparse random graphs, we find empirically that the distribution of
the cut sizes found by ``local'' algorithms becomes peaked as the number of
vertices in the graphs becomes large. Evidence is given that this distribution
tends towards a Gaussian whose mean and variance scales linearly with the
number of vertices of the graphs. Given the distribution of cut sizes
associated with each heuristic, we provide a ranking procedure which takes into
account both the quality of the solutions and the speed of the algorithms. This
procedure is demonstrated for a selection of local graph bisection heuristics.Comment: 17 pages, 5 figures, submitted to SIAM Journal on Optimization also
available at http://ipnweb.in2p3.fr/~martin
Non-homogeneous polygonal Markov fields in the plane: graphical representations and geometry of higher order correlations
We consider polygonal Markov fields originally introduced by Arak and
Surgailis (1989). Our attention is focused on fields with nodes of order two,
which can be regarded as continuum ensembles of non-intersecting contours in
the plane, sharing a number of features with the two-dimensional Ising model.
We introduce non-homogeneous version of polygonal fields in anisotropic
enviroment. For these fields we provide a class of new graphical constructions
and random dynamics. These include a generalised dynamic representation,
generalised and defective disagreement loop dynamics as well as a generalised
contour birth and death dynamics. Next, we use these constructions as tools to
obtain new exact results on the geometry of higher order correlations of
polygonal Markov fields in their consistent regime.Comment: 54 page
Highly parallel sparse Cholesky factorization
Several fine grained parallel algorithms were developed and compared to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed memory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special purpose algorithms in which the matrix structure conforms to the connection structure of the machine, the focus is on matrices with arbitrary sparsity structure. The most promising algorithm is one whose inner loop performs several dense factorizations simultaneously on a 2-D grid of processors. Virtually any massively parallel dense factorization algorithm can be used as the key subroutine. The sparse code attains execution rates comparable to those of the dense subroutine. Although at present architectural limitations prevent the dense factorization from realizing its potential efficiency, it is concluded that a regular data parallel architecture can be used efficiently to solve arbitrarily structured sparse problems. A performance model is also presented and it is used to analyze the algorithms
Transport properties near the Anderson transition
The electronic transport properties in the presence of a temperature gradient
in disordered systems near the metal-insulator transition [MIT] are considered.
The d.c. conductivity , the thermoelectric power , the thermal
conductivity and the Lorenz number are calculated for the
three-dimensional Anderson model of localization using the
Chester-Thellung-Kubo-Greenwood formulation of linear response. We show that
, S, K and can be scaled to one-parameter scaling curves with a
single scaling paramter .Comment: 4 pages, 4 EPS figures, uses annalen.cls style [included]; presented
at Localization 1999, to appear in Annalen der Physik [supplement
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