4,997 research outputs found
A Shortcut to the Q-Operator
Baxter's Q-operator is generally believed to be the most powerful tool for
the exact diagonalization of integrable models. Curiously, it has hitherto not
yet been properly constructed in the simplest such system, the compact spin-1/2
Heisenberg-Bethe XXX spin chain. Here we attempt to fill this gap and show how
two linearly independent operatorial solutions to Baxter's TQ equation may be
constructed as commuting transfer matrices if a twist field is present. The
latter are obtained by tracing over infinitely many oscillator states living in
the auxiliary channel of an associated monodromy matrix. We furthermore compare
and differentiate our approach to earlier articles addressing the problem of
the construction of the Q-operator for the XXX chain. Finally we speculate on
the importance of Q-operators for the physical interpretation of recent
proposals for the Y-system of AdS/CFT.Comment: 41 pages, 2 figures; v2: references added; v3: version published in
J. Stat. Mec
Star-Triangle Relation for a Three Dimensional Model
The solvable -chiral Potts model can be interpreted as a
three-dimensional lattice model with local interactions. To within a minor
modification of the boundary conditions it is an Ising type model on the body
centered cubic lattice with two- and three-spin interactions. The corresponding
local Boltzmann weights obey a number of simple relations, including a
restricted star-triangle relation, which is a modified version of the
well-known star-triangle relation appearing in two-dimensional models. We show
that these relations lead to remarkable symmetry properties of the Boltzmann
weight function of an elementary cube of the lattice, related to spatial
symmetry group of the cubic lattice. These symmetry properties allow one to
prove the commutativity of the row-to-row transfer matrices, bypassing the
tetrahedron relation. The partition function per site for the infinite lattice
is calculated exactly.Comment: 20 pages, plain TeX, 3 figures, SMS-079-92/MRR-020-92. (corrupted
figures replaced
Predicting human preferences using the block structure of complex social networks
With ever-increasing available data, predicting individuals' preferences and
helping them locate the most relevant information has become a pressing need.
Understanding and predicting preferences is also important from a fundamental
point of view, as part of what has been called a "new" computational social
science. Here, we propose a novel approach based on stochastic block models,
which have been developed by sociologists as plausible models of complex
networks of social interactions. Our model is in the spirit of predicting
individuals' preferences based on the preferences of others but, rather than
fitting a particular model, we rely on a Bayesian approach that samples over
the ensemble of all possible models. We show that our approach is considerably
more accurate than leading recommender algorithms, with major relative
improvements between 38% and 99% over industry-level algorithms. Besides, our
approach sheds light on decision-making processes by identifying groups of
individuals that have consistently similar preferences, and enabling the
analysis of the characteristics of those groups
The QCD Pomeron in ultraperipheral heavy ion collisions: III. Photonuclear production of heavy quarks
We calculate the photonuclear production of heavy quarks in ultraperipheral
heavy ion collisions. The integrated cross section and the rapidity
distribution are computed employing sound high energy QCD formalisms as the
collinear and semihard approaches as well as the saturation model. In
particular, the color glass condensate (CGC) formalism is also considered using
a simple phenomenological parameterization for the color field correlator in
the medium, which allow us to obtain more reliable estimates for charm and
bottom production at
LHC energies.Comment: 15 pages, 2 figures. Extended version to be published in Eur. Phys.
J.
Spectral quark model and low-energy hadron phenomenology
We propose a spectral quark model which can be applied to low energy hadronic
physics. The approach is based on a generalization of the Lehmann
representation of the quark propagator. We work at the one-quark-loop level.
Electromagnetic and chiral invariance are ensured with help of the gauge
technique which provides particular solutions to the Ward-Takahashi identities.
General conditions on the quark spectral function follow from natural physical
requirements. In particular, the function is normalized, its all positive
moments must vanish, while the physical observables depend on negative moments
and the so-called log-moments. As a consequence, the model is made finite,
dispersion relations hold, chiral anomalies are preserved, and the twist
expansion is free from logarithmic scaling violations, as requested of a
low-energy model. We study a variety of processes and show that the framework
is very simple and practical. Finally, incorporating the idea of vector-meson
dominance, we present an explicit construction of the quark spectral function
which satisfies all the requirements. The corresponding momentum representation
of the resulting quark propagator exhibits only cuts on the physical axis, with
no poles present anywhere in the complex momentum space. The momentum-dependent
quark mass compares very well to recent lattice calculations. A large number of
predictions and relations can be deduced from our approach for such quantities
as the pion light-cone wave function, non-local quark condensate, pion
transition form factor, pion valence parton distribution function, etc.Comment: revtex, 24 pages, 3 figure
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