2,618 research outputs found
Magnetic-Field Induced First-Order Transition in the Frustrated XY Model on a Stacked Triangular Lattice
The results of extensive Monte Carlo simulations of magnetic-field induced
transitions in the xy model on a stacked triangular lattice with
antiferromagnetic intraplane and ferromagnetic interplane interactions are
discussed. A low-field transition from the paramagnetic to a 3-state (Potts)
phase is found to be very weakly first order with behavior suggesting
tricriticality at zero field. In addition to clarifying some long-standing
ambiguity concerning the nature of this Potts-like transition, the present work
also serves to further our understanding of the critical behavior at ,
about which there has been much controversy.Comment: 10 pages (RevTex 3.0), 4 figures available upon request, CRPS-93-0
A simpler and more efficient algorithm for the next-to-shortest path problem
Given an undirected graph with positive edge lengths and two
vertices and , the next-to-shortest path problem is to find an -path
which length is minimum amongst all -paths strictly longer than the
shortest path length. In this paper we show that the problem can be solved in
linear time if the distances from and to all other vertices are given.
Particularly our new algorithm runs in time for general
graphs, which improves the previous result of time for sparse
graphs, and takes only linear time for unweighted graphs, planar graphs, and
graphs with positive integer edge lengths.Comment: Partial result appeared in COCOA201
Level-Spacing Distributions and the Bessel Kernel
The level spacing distributions which arise when one rescales the Laguerre or
Jacobi ensembles of hermitian matrices is studied. These distributions are
expressible in terms of a Fredholm determinant of an integral operator whose
kernel is expressible in terms of Bessel functions of order . We derive
a system of partial differential equations associated with the logarithmic
derivative of this Fredholm determinant when the underlying domain is a union
of intervals. In the case of a single interval this Fredholm determinant is a
Painleve tau function.Comment: 18 pages, resubmitted to make postscript compatible, no changes to
manuscript conten
Arithmetically Cohen-Macaulay Bundles on complete intersection varieties of sufficiently high multidegree
Recently it has been proved that any arithmetically Cohen-Macaulay (ACM)
bundle of rank two on a general, smooth hypersurface of degree at least three
and dimension at least four is a sum of line bundles. When the dimension of the
hypersurface is three, a similar result is true provided the degree of the
hypersurface is at least six. We extend these results to complete intersection
subvarieties by proving that any ACM bundle of rank two on a general, smooth
complete intersection subvariety of sufficiently high multi-degree and
dimension at least four splits. We also obtain partial results in the case of
threefolds.Comment: 15 page
An Empirical Process Central Limit Theorem for Multidimensional Dependent Data
Let be the empirical process associated to an
-valued stationary process . We give general conditions,
which only involve processes for a restricted class of
functions , under which weak convergence of can be
proved. This is particularly useful when dealing with data arising from
dynamical systems or functional of Markov chains. This result improves those of
[DDV09] and [DD11], where the technique was first introduced, and provides new
applications.Comment: to appear in Journal of Theoretical Probabilit
Search for a Standard Model Higgs Boson in CMS via Vector Boson Fusion in the H->WW->l\nu l\nu Channel
We present the potential for discovering the Standard Model Higgs boson
produced by the vector-boson fusion mechanism. We considered the decay of Higgs
bosons into the W+W- final state, with both W-bosons subsequently decaying
leptonically. The main background is ttbar with one or more jets produced. This
study is based on a full simulation of the CMS detector, and up-to-date
reconstruction codes. The result is that a signal of 5 sigma significance can
be obtained with an integrated luminosity of 12-72 1/fb for Higgs boson masses
between 130-200 GeV. In addition, the major background can be measured directly
to 7% from the data with an integrated luminosity of 30 1/fb. In this study, we
also suggested a method to obtain information in Higgs mass using the
transverse mass distributions.Comment: 26 pages, 22 figure
Number--conserving model for boson pairing
An independent pair ansatz is developed for the many body wavefunction of
dilute Bose systems. The pair correlation is optimized by minimizing the
expectation value of the full hamiltonian (rather than the truncated Bogoliubov
one) providing a rigorous energy upper bound. In contrast with the Jastrow
model, hypernetted chain theory provides closed-form exactly solvable equations
for the optimized pair correlation. The model involves both condensate and
coherent pairing with number conservation and kinetic energy sum rules
satisfied exactly and the compressibility sum rule obeyed at low density. We
compute, for bulk boson matter at a given density and zero temperature, (i) the
two--body distribution function, (ii) the energy per particle, (iii) the sound
velocity, (iv) the chemical potential, (v) the momentum distribution and its
condensate fraction and (vi) the pairing function, which quantifies the ODLRO
resulting from the structural properties of the two--particle density matrix.
The connections with the low--density expansion and Bogoliubov theory are
analyzed at different density values, including the density and scattering
length regime of interest of trapped-atoms Bose--Einstein condensates.
Comparison with the available Diffusion Monte Carlo results is also made.Comment: 21 pages, 12 figure
Fredholm Determinants, Differential Equations and Matrix Models
Orthogonal polynomial random matrix models of NxN hermitian matrices lead to
Fredholm determinants of integral operators with kernel of the form (phi(x)
psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm
determinants of integral operators having kernel of this form and where the
underlying set is a union of open intervals. The emphasis is on the
determinants thought of as functions of the end-points of these intervals. We
show that these Fredholm determinants with kernels of the general form
described above are expressible in terms of solutions of systems of PDE's as
long as phi and psi satisfy a certain type of differentiation formula. There is
also an exponential variant of this analysis which includes the circular
ensembles of NxN unitary matrices.Comment: 34 pages, LaTeX using RevTeX 3.0 macros; last version changes only
the abstract and decreases length of typeset versio
MHV Vertices and Scattering Amplitudes in Gauge Theory
The generic googly amplitudes in gauge theory are computed by using the
Cachazo-Svrcek-Witten approach to perturbative calculation in gauge theory and
the results are in agreement with the previously well-known ones. Within this
approach we also discuss the parity transformation, charge conjugation and the
dual Ward identity. We also extend this calculation to include fermions and the
googly amplitudes with a single quark-anti-quark pair are obtained correctly
from fermionic MHV vertices. At the end we briefly discuss the possible
extension of this approach to gravity.Comment: Latex file, 38 pages, 15 figures; v2, minor changes, references
added; v2, minor changes, 2 references adde
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