3,423 research outputs found
Site dilution of quantum spins in the honeycomb lattice
We discuss the effect of site dilution on both the magnetization and the
density of states of quantum spins in the honeycomb lattice, described by the
antiferromagnetic Heisenberg spin-S model. For this purpose a real-space
Bogoliubov-Valatin transformation is used. In this work we show that for the
S>1/2 the system can be analyzed in terms of linear spin wave theory. For spin
S=1/2, however, the linear spin wave approximation breaks down. In this case,
we have studied the effect of dilution on the staggered magnetization using the
Stochastic Series Expansion Monte Carlo method. Two main results are to be
stressed from the Monte Carlo method: (i) a better value for the staggered
magnetization of the undiluted system, m=0.2677(6); (ii) a finite value of the
staggered magnetization of the percolating cluster at the classical percolation
threshold, showing that there is no quantum critical transition driven by
dilution in the Heisenberg model. In the solution of the problem using linear
the spin wave method we pay special attention to the presence of zero energy
modes. Using a combination of linear spin wave analysis and the recursion
method we were able to obtain the thermodynamic limit behavior of the density
of states for both the square and the honeycomb lattices. We have used both the
staggered magnetization and the density of states to analyze neutron scattering
experiments and Neel temperature measurements on quasi-two- -dimensional
honeycomb systems. Our results are in quantitative agreement with experimental
results on Mn_pZn_{1-p}PS_3 and on the Ba(Ni_pMg_{1-p})_2V_2O_8.Comment: 21 pages (REVTEX), 16 figure
Hadron Mass Predictions of the Valence Approximation to Lattice QCD
We evaluate the infinite volume, continuum limits of eight hadron mass ratios
predicted by lattice QCD with Wilson quarks in the valence (quenched)
approximation. Each predicted ratio differs from the corresponding observed
value by less than 6\%.Comment: 13 pages of Latex + 2 PostScript files attached, IBM/HET 92-
Meson Decay Constants from the Valence Approximation to Lattice QCD
We evaluate , , , and , extrapolated to physical quark mass, zero
lattice spacing and infinite volume, for lattice QCD with Wilson quarks in the
valence (quenched) approximation. The predicted ratios differ from experiment
by amounts ranging from 12\% to 17\% equivalent to between 0.9 and 2.8 times
the corresponding statistical uncertainties.Comment: uufiles encoded copy of 40 page Latex article, including 14 figures
in Postscript. The long version of hep-lat/9302012, IBM/HET 93-
Hierarchically nested factor model from multivariate data
We show how to achieve a statistical description of the hierarchical
structure of a multivariate data set. Specifically we show that the similarity
matrix resulting from a hierarchical clustering procedure is the correlation
matrix of a factor model, the hierarchically nested factor model. In this
model, factors are mutually independent and hierarchically organized. Finally,
we use a bootstrap based procedure to reduce the number of factors in the model
with the aim of retaining only those factors significantly robust with respect
to the statistical uncertainty due to the finite length of data records.Comment: 7 pages, 5 figures; accepted for publication in Europhys. Lett. ; the
Appendix corresponds to the additional material of the accepted letter
Two spin liquid phases in the spatially anisotropic triangular Heisenberg model
The quantum spin-1/2 antiferromagnetic Heisenberg model on a two dimensional
triangular lattice geometry with spatial anisotropy is relevant to describe
materials like and organic compounds like
{-(ET)Cu(CN)}. The strength of the spatial anisotropy can
increase quantum fluctuations and can destabilize the magnetically ordered
state leading to non conventional spin liquid phases. In order to understand
these intriguing phenomena, quantum Monte Carlo methods are used to study this
model system as a function of the anisotropic strength, represented by the
ratio between the intra-chain nearest neighbor coupling and the
inter-chain one . We have found evidence of two spin liquid regions. The
first one is stable for small values of the coupling J'/J \alt 0.65, and
appears gapless and fractionalized, whereas the second one is a more
conventional spin liquid with a small spin gap and is energetically favored in
the region 0.65\alt J'/J \alt 0.8. We have also shown that in both spin
liquid phases there is no evidence of broken translation symmetry with dimer or
spin-Peirls order or any broken spatial reflection symmetry of the lattice. The
various phases are in good agreement with the experimental findings, thus
supporting the existence of spin liquid phases in two dimensional quantum
spin-1/2 systems.Comment: 35 pages, 24 figures, 3 table
Universality of rain event size distributions
We compare rain event size distributions derived from measurements in
climatically different regions, which we find to be well approximated by power
laws of similar exponents over broad ranges. Differences can be seen in the
large-scale cutoffs of the distributions. Event duration distributions suggest
that the scale-free aspects are related to the absence of characteristic scales
in the meteorological mesoscale.Comment: 16 pages, 10 figure
High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition
This paper presents a novel adaptive-sparse polynomial dimensional
decomposition (PDD) method for stochastic design optimization of complex
systems. The method entails an adaptive-sparse PDD approximation of a
high-dimensional stochastic response for statistical moment and reliability
analyses; a novel integration of the adaptive-sparse PDD approximation and
score functions for estimating the first-order design sensitivities of the
statistical moments and failure probability; and standard gradient-based
optimization algorithms. New analytical formulae are presented for the design
sensitivities that are simultaneously determined along with the moments or the
failure probability. Numerical results stemming from mathematical functions
indicate that the new method provides more computationally efficient design
solutions than the existing methods. Finally, stochastic shape optimization of
a jet engine bracket with 79 variables was performed, demonstrating the power
of the new method to tackle practical engineering problems.Comment: 18 pages, 2 figures, to appear in Sparse Grids and
Applications--Stuttgart 2014, Lecture Notes in Computational Science and
Engineering 109, edited by J. Garcke and D. Pfl\"{u}ger, Springer
International Publishing, 201
Optimal discrete stopping times for reliability growth tests
Often, the duration of a reliability growth development test is specified in advance and the decision to terminate or continue testing is conducted at discrete time intervals. These features are normally not captured by reliability growth models. This paper adapts a standard reliability growth model to determine the optimal time for which to plan to terminate testing. The underlying stochastic process is developed from an Order Statistic argument with Bayesian inference used to estimate the number of faults within the design and classical inference procedures used to assess the rate of fault detection. Inference procedures within this framework are explored where it is shown the Maximum Likelihood Estimators possess a small bias and converges to the Minimum Variance Unbiased Estimator after few tests for designs with moderate number of faults. It is shown that the Likelihood function can be bimodal when there is conflict between the observed rate of fault detection and the prior distribution describing the number of faults in the design. An illustrative example is provided
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