831 research outputs found
Percolation in three-dimensional random field Ising magnets
The structure of the three-dimensional random field Ising magnet is studied
by ground state calculations. We investigate the percolation of the minority
spin orientation in the paramagnetic phase above the bulk phase transition,
located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the
Gaussian random fields (J=1). With an external field H there is a disorder
strength dependent critical field +/- H_c(Delta) for the down (or up) spin
spanning. The percolation transition is in the standard percolation
universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/-
0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <=
Delta_p. When, with zero external field, Delta is decreased from a large value
there is a transition from the simultaneous up and down spin spanning, with
probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This
is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster
has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta).
We provide evidence that this is asymptotically true even at H=0 for Delta_c <
Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is
approached from above. Percolation implies extra finite size effects in the
ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review
Formation of Small-Scale Condensations in the Molecular Clouds via Thermal Instability
A systematic study of the linear thermal instability of a self-gravitating
magnetic molecular cloud is carried out for the case when the unperturbed
background is subject to local expansion or contraction. We consider the
ambipolar diffusion, or ion-neutral friction on the perturbed states. In this
way, we obtain a non-dimensional characteristic equation that reduces to the
prior characteristic equation in the non-gravitating stationary background. By
parametric manipulation of this characteristic equation, we conclude that there
are, not only oblate condensation forming solutions, but also prolate solutions
according to local expansion or contraction of the background. We obtain the
conditions for existence of the Field lengths that thermal instability in the
molecular clouds can occur. If these conditions establish, small-scale
condensations in the form of spherical, oblate, or prolate may be produced via
thermal instability.Comment: 16 page, accepted by Ap&S
Effects of Pore Walls and Randomness on Phase Transitions in Porous Media
We study spin models within the mean field approximation to elucidate the
topology of the phase diagrams of systems modeling the liquid-vapor transition
and the separation of He--He mixtures in periodic porous media. These
topologies are found to be identical to those of the corresponding random field
and random anisotropy spin systems with a bimodal distribution of the
randomness. Our results suggest that the presence of walls (periodic or
otherwise) are a key factor determining the nature of the phase diagram in
porous media.Comment: REVTeX, 11 eps figures, to appear in Phys. Rev.
The Random Quadratic Assignment Problem
Optimal assignment of classes to classrooms \cite{dickey}, design of DNA
microarrays \cite{carvalho}, cross species gene analysis \cite{kolar}, creation
of hospital layouts cite{elshafei}, and assignment of components to locations
on circuit boards \cite{steinberg} are a few of the many problems which have
been formulated as a quadratic assignment problem (QAP). Originally formulated
in 1957, the QAP is one of the most difficult of all combinatorial optimization
problems. Here, we use statistical mechanical methods to study the asymptotic
behavior of problems in which the entries of at least one of the two matrices
that specify the problem are chosen from a random distribution .
Surprisingly, this case has not been studied before using statistical methods
despite the fact that the QAP was first proposed over 50 years ago
\cite{Koopmans}. We find simple forms for and , the
costs of the minimal and maximum solutions respectively. Notable features of
our results are the symmetry of the results for and
and the dependence on only through its mean and standard deviation,
independent of the details of . After the asymptotic cost is determined for
a given QAP problem, one can straightforwardly calculate the asymptotic cost of
a QAP problem specified with a different random distribution
Active Galactic Nuclei at the Crossroads of Astrophysics
Over the last five decades, AGN studies have produced a number of spectacular
examples of synergies and multifaceted approaches in astrophysics. The field of
AGN research now spans the entire spectral range and covers more than twelve
orders of magnitude in the spatial and temporal domains. The next generation of
astrophysical facilities will open up new possibilities for AGN studies,
especially in the areas of high-resolution and high-fidelity imaging and
spectroscopy of nuclear regions in the X-ray, optical, and radio bands. These
studies will address in detail a number of critical issues in AGN research such
as processes in the immediate vicinity of supermassive black holes, physical
conditions of broad-line and narrow-line regions, formation and evolution of
accretion disks and relativistic outflows, and the connection between nuclear
activity and galaxy evolution.Comment: 16 pages, 5 figures; review contribution; "Exploring the Cosmic
Frontier: Astrophysical Instruments for the 21st Century", ESO Astrophysical
Symposia Serie
Critical aspects of the random-field Ising model
We investigate the critical behavior of the three-dimensional random-field Ising model
(RFIM) with a Gaussian field distribution at zero temperature. By implementing a
computational approach that maps the ground-state of the RFIM to the maximum-flow
optimization problem of a network, we simulate large ensembles of disorder realizations of
the model for a broad range of values of the disorder strength h and
system sizes = L3, with L ≤ 156. Our averaging procedure
outcomes previous studies of the model, increasing the sampling of ground states by a
factor of 103. Using well-established finite-size scaling schemes, the
fourth-order’s Binder cumulant, and the sample-to-sample fluctuations of various
thermodynamic quantities, we provide high-accuracy estimates for the critical field
hc, as well as the critical exponents ν,
β/ν, and γ̅/ν of the correlation length, order parameter, and
disconnected susceptibility, respectively. Moreover, using properly defined noise to
signal ratios, we depict the variation of the self-averaging property of the model, by
crossing the phase boundary into the ordered phase. Finally, we discuss the controversial
issue of the specific heat based on a scaling analysis of the bond energy, providing
evidence that its critical exponent α ≈ 0−
First Measurement of Z/gamma* Production in Compton Scattering of Quasi-real Photons
We report the first observation of Z/gamma* production in Compton scattering
of quasi-real photons. This is a subprocess of the reaction e+e- to
e+e-Z/gamma*, where one of the final state electrons is undetected.
Approximately 55 pb-1 of data collected in the year 1997 at an e+e-
centre-of-mass energy of 183 GeV with the OPAL detector at LEP have been
analysed. The Z/gamma* from Compton scattering has been detected in the
hadronic decay channel. Within well defined kinematic bounds, we measure the
product of cross-section and Z/gamma* branching ratio to hadrons to be
(0.9+-0.3+-0.1) pb for events with a hadronic mass larger than 60 GeV,
dominated by (e)eZ production. In the hadronic mass region between 5 GeV and 60
GeV, dominated by (e)egamma* production, this product is found to be
(4.1+-1.6+-0.6) pb. Our results agree with the predictions of two Monte Carlo
event generators, grc4f and PYTHIA.Comment: 18 pages, LaTeX, 5 eps figures included, submitted to Physics Letters
Observation of hard scattering in photoproduction events with a large rapidity gap at HERA
Events with a large rapidity gap and total transverse energy greater than 5
GeV have been observed in quasi-real photoproduction at HERA with the ZEUS
detector. The distribution of these events as a function of the
centre of mass energy is consistent with diffractive scattering. For total
transverse energies above 12 GeV, the hadronic final states show predominantly
a two-jet structure with each jet having a transverse energy greater than 4
GeV. For the two-jet events, little energy flow is found outside the jets. This
observation is consistent with the hard scattering of a quasi-real photon with
a colourless object in the proton.Comment: 19 pages, latex, 4 figures appended as uuencoded fil
Search for Higgs Bosons in e+e- Collisions at 183 GeV
The data collected by the OPAL experiment at sqrts=183 GeV were used to
search for Higgs bosons which are predicted by the Standard Model and various
extensions, such as general models with two Higgs field doublets and the
Minimal Supersymmetric Standard Model (MSSM). The data correspond to an
integrated luminosity of approximately 54pb-1. None of the searches for neutral
and charged Higgs bosons have revealed an excess of events beyond the expected
background. This negative outcome, in combination with similar results from
searches at lower energies, leads to new limits for the Higgs boson masses and
other model parameters. In particular, the 95% confidence level lower limit for
the mass of the Standard Model Higgs boson is 88.3 GeV. Charged Higgs bosons
can be excluded for masses up to 59.5 GeV. In the MSSM, mh > 70.5 GeV and mA >
72.0 GeV are obtained for tan{beta}>1, no and maximal scalar top mixing and
soft SUSY-breaking masses of 1 TeV. The range 0.8 < tanb < 1.9 is excluded for
minimal scalar top mixing and m{top} < 175 GeV. More general scans of the MSSM
parameter space are also considered.Comment: 49 pages. LaTeX, including 33 eps figures, submitted to European
Physical Journal
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