4,603 research outputs found
Loop Model with Generalized Fugacity in Three Dimensions
A statistical model of loops on the three-dimensional lattice is proposed and
is investigated. It is O(n)-type but has loop fugacity that depends on global
three-dimensional shapes of loops in a particular fashion. It is shown that,
despite this non-locality and the dimensionality, a layer-to-layer transfer
matrix can be constructed as a product of local vertex weights for infinitely
many points in the parameter space. Using this transfer matrix, the site
entropy is estimated numerically in the fully packed limit.Comment: 16pages, 4 eps figures, (v2) typos and Table 3 corrected. Refs added,
(v3) an error in an explanation of fig.2 corrected. Refs added. (v4) Changes
in the presentatio
On the universality of compact polymers
Fully packed loop models on the square and the honeycomb lattice constitute
new classes of critical behaviour, distinct from those of the low-temperature
O(n) model. A simple symmetry argument suggests that such compact phases are
only possible when the underlying lattice is bipartite. Motivated by the hope
of identifying further compact universality classes we therefore study the
fully packed loop model on the square-octagon lattice. Surprisingly, this model
is only critical for loop weights n < 1.88, and its scaling limit coincides
with the dense phase of the O(n) model. For n=2 it is exactly equivalent to the
selfdual 9-state Potts model. These analytical predictions are confirmed by
numerical transfer matrix results. Our conclusions extend to a large class of
bipartite decorated lattices.Comment: 13 pages including 4 figure
Radiation reaction on charged particles in three-dimensional motion in classical and quantum electrodynamics
We extend our previous work (see arXiv:quant-ph/0501026), which compared the
predictions of quantum electrodynamics concerning radiation reaction with those
of the Abraham-Lorentz-Dirac theory for a charged particle in linear motion.
Specifically, we calculate the predictions for the change in position of a
charged scalar particle, moving in three-dimensional space, due to the effect
of radiation reaction in the one-photon-emission process in quantum
electrodynamics. The scalar particle is assumed to be accelerated for a finite
period of time by a three-dimensional electromagnetic potential dependent only
on one of the spacetime coordinates. We perform this calculation in the
limit and show that the change in position agrees with that
obtained in classical electrodynamics with the Lorentz-Dirac force treated as a
perturbation. We also show for a time-dependent but space-independent
electromagnetic potential that the forward-scattering amplitude at order
does not contribute to the position change in the limit after the
mass renormalization is taken into account.Comment: Latex, 20page
The packing of two species of polygons on the square lattice
We decorate the square lattice with two species of polygons under the
constraint that every lattice edge is covered by only one polygon and every
vertex is visited by both types of polygons. We end up with a 24 vertex model
which is known in the literature as the fully packed double loop model. In the
particular case in which the fugacities of the polygons are the same, the model
admits an exact solution. The solution is obtained using coordinate Bethe
ansatz and provides a closed expression for the free energy. In particular we
find the free energy of the four colorings model and the double Hamiltonian
walk and recover the known entropy of the Ice model. When both fugacities are
set equal to two the model undergoes an infinite order phase transition.Comment: 21 pages, 4 figure
CBR Temperature Fluctuations Induced by Gravitational Waves in a Spatially-Closed Inflationary Universe
Primordial gravitational waves are created during the de Sitter phase of an
exponentially-expanding (inflationary) universe, due to quantum zero-point
vacuum fluctuations. These waves produce fluctuations in the temperature of the
Cosmic Background Radiation (CBR). We calculate the multipole moments of the
correlation function for these temperature fluctuations in a spatially-closed
Friedman-Robertson-Walker (FRW) cosmological model. The results are compared to
the corresponding multipoles in the spatially-flat case. The differences are
small unless the density parameter today, , is greater than 2.
(Submitted to Physical Review D).Comment: 18 pages of RevTex + 3 uuencoded postscript figure
Scalar Field Quantum Inequalities in Static Spacetimes
We discuss quantum inequalities for minimally coupled scalar fields in static
spacetimes. These are inequalities which place limits on the magnitude and
duration of negative energy densities. We derive a general expression for the
quantum inequality for a static observer in terms of a Euclidean two-point
function. In a short sampling time limit, the quantum inequality can be written
as the flat space form plus subdominant correction terms dependent upon the
geometric properties of the spacetime. This supports the use of flat space
quantum inequalities to constrain negative energy effects in curved spacetime.
Using the exact Euclidean two-point function method, we develop the quantum
inequalities for perfectly reflecting planar mirrors in flat spacetime. We then
look at the quantum inequalities in static de~Sitter spacetime, Rindler
spacetime and two- and four-dimensional black holes. In the case of a
four-dimensional Schwarzschild black hole, explicit forms of the inequality are
found for static observers near the horizon and at large distances. It is show
that there is a quantum averaged weak energy condition (QAWEC), which states
that the energy density averaged over the entire worldline of a static observer
is bounded below by the vacuum energy of the spacetime. In particular, for an
observer at a fixed radial distance away from a black hole, the QAWEC says that
the averaged energy density can never be less than the Boulware vacuum energy
density.Comment: 27 pages, 2 Encapsulated Postscript figures, uses epsf.tex, typeset
in RevTe
Weak gravity in DGP braneworld model
We analyze the weak gravity in the braneworld model proposed by
Dvali-Gabadadze-Porrati, in which the unperturbed background spacetime is given
by five dimensional Minkowski bulk with a brane which has the induced Einstein
Hilbert term. This model has a critical length scale . Naively, we expect
that the four dimensional general relativity (4D GR) is approximately recovered
at the scale below . However, the simple linear perturbation does not work
in this regime. Only recently the mechanism to recover 4D GR was clarified
under the restriction to spherically symmetric configurations, and the leading
correction to 4D GR was derived. Here, we develop an alternative formulation
which can handle more general perturbations. We also generalize the model by
adding bulk cosmological constant and the brane tension.Comment: 7 pages, 1 figure, references adde
Random-cluster representation of the Blume-Capel model
The so-called diluted-random-cluster model may be viewed as a random-cluster
representation of the Blume--Capel model. It has three parameters, a vertex
parameter , an edge parameter , and a cluster weighting factor .
Stochastic comparisons of measures are developed for the `vertex marginal' when
, and the `edge marginal' when q\in[1,\oo). Taken in conjunction
with arguments used earlier for the random-cluster model, these permit a
rigorous study of part of the phase diagram of the Blume--Capel model
On Infrared Effects in de~Sitter Background
We have estimated higher order quantum gravity corrections to de~Sitter
spacetime. Our results suggest that, while the classical spacetime metric may
be distorted by the graviton self-interactions, the corrections are relatively
weaker than previously thought, possibly growing like a power rather than
exponentially in time.Comment: 17, UM-TH-94-11, (1 postscript fig. at end
Scalar radiation emitted from a source rotating around a black hole
We analyze the scalar radiation emitted from a source rotating around a
Schwarzschild black hole using the framework of quantum field theory at the
tree level. We show that for relativistic circular orbits the emitted power is
about 20% to 30% smaller than what would be obtained in Minkowski spacetime. We
also show that most of the emitted energy escapes to infinity. Our formalism
can readily be adapted to investigate similar processes.Comment: 19 pages (REVTEX), 5 figures, title slightly changed, extra
demonstration and minor improvements included. To appear in Class. Quant.
Gra
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