6,542 research outputs found
High precision Monte Carlo study of the 3D XY-universality class
We present a Monte Carlo study of the two-component model on the
simple cubic lattice in three dimensions. By suitable tuning of the coupling
constant we eliminate leading order corrections to scaling. High
statistics simulations using finite size scaling techniques yield
and , where the statistical and
systematical errors are given in the first and second bracket, respectively.
These results are more precise than any previous theoretical estimate of the
critical exponents for the 3D XY universality class.Comment: 13 page
Optimized Perturbation Theory for Wave Functions of Quantum Systems
The notion of the optimized perturbation, which has been successfully applied
to energy eigenvalues, is generalized to treat wave functions of quantum
systems. The key ingredient is to construct an envelope of a set of
perturbative wave functions. This leads to a condition similar to that obtained
from the principle of minimal sensitivity. Applications of the method to
quantum anharmonic oscillator and the double well potential show that uniformly
valid wave functions with correct asymptotic behavior are obtained in the
first-order optimized perturbation even for strong couplings.Comment: 11 pages, RevTeX, three ps figure
New Algorithm of the Finite Lattice Method for the High-temperature Expansion of the Ising Model in Three Dimensions
We propose a new algorithm of the finite lattice method to generate the
high-temperature series for the Ising model in three dimensions. It enables us
to extend the series for the free energy of the simple cubic lattice from the
previous series of 26th order to 46th order in the inverse temperature. The
obtained series give the estimate of the critical exponent for the specific
heat in high precision.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Letter
Quantum Dynamics of the Slow Rollover Transition in the Linear Delta Expansion
We apply the linear delta expansion to the quantum mechanical version of the
slow rollover transition which is an important feature of inflationary models
of the early universe. The method, which goes beyond the Gaussian
approximation, gives results which stay close to the exact solution for longer
than previous methods. It provides a promising basis for extension to a full
field theoretic treatment.Comment: 12 pages, including 4 figure
Transition temperature of a dilute homogeneous imperfect Bose gas
The leading-order effect of interactions on a homogeneous Bose gas is
theoretically predicted to shift the critical temperature by an amount
\Delta\Tc = # a_{scatt} n^{1/3} T_0 from the ideal gas result T_0, where
a_{scatt} is the scattering length and n is the density. There have been
several different theoretical estimates for the numerical coefficient #. We
claim to settle the issue by measuring the numerical coefficient in a lattice
simulation of O(2) phi^4 field theory in three dimensions---an effective theory
which, as observed previously in the literature, can be systematically matched
to the dilute Bose gas problem to reproduce non-universal quantities such as
the critical temperature. We find # = 1.32 +- 0.02.Comment: 4 pages, submitted to Phys. Rev. Lett; minor changes due to
improvement of analysis in the longer companion pape
Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0
We simulate self-avoiding walks on a cubic lattice and determine the second
virial coefficient for walks of different lengths. This allows us to determine
the critical value of the renormalized four-point coupling constant in the
three-dimensional N-vector universality class for N=0. We obtain g* =
1.4005(5), where g is normalized so that the three-dimensional
field-theoretical beta-function behaves as \beta(g) = - g + g^2 for small g. As
a byproduct, we also obtain precise estimates of the interpenetration ratio
Psi*, Psi* = 0.24685(11), and of the exponent \nu, \nu = 0.5876(2).Comment: 16 page
Calcium and Zinc Ion Release from Polyalkenoate Cements Formed from Zinc Oxide/apatite Mixtures
Calcium and zinc ion release from hydroxyapatite-zinc oxide-poly (acrylic acid) (HAZnO-PAA) composite cements into deionised water was investigated as a function of HA content, PAA concentration, PAA molecular weight and maturation time. At any given maturation time, zinc ion release was constant until the HA content was at the maximum loading (60 wt%) resulting in the cement matrix breaking up, allowing exacerbated ion release. The calcium ion release increased with increased HA content in the composite until the maximum loading where the release drops off. Up to this point, the release of both ionic species was proportional to square root time for the initial 24-hour period, indicating that the release is diffusion controlled. In agreement with related data from conventional Glass Polyalkenoate Cements (GPCs), it is the concentration of the PAA, not the molecular weight, that influences ion release from these materials. However, unlike GPCs, the release of the active ions results in a pH rise in the deionised water, more conventionally seen with Bioglass® and related bioactive glasses. It is this pH rise, caused by the ion exchange of Zn2+ and Ca2+ for H+ from the water, leaving an excess of OH-, that should result in a favourable bioactive response both in vitro and in-vivo. © Springer Science + Business Media, LLC 2006
Time Uncertainty in Quantum Gravitational Systems
It is generally argued that the combined effect of Heisenberg principle and
general relativity leads to a minimum time uncertainty. Most of the analyses
supporting this conclusion are based on a perturbative approach to
quantization. We consider a simple family of gravitational models, including
the Einstein-Rosen waves, in which the (non-linearized) inclusion of gravity
changes the normalization of time translations by a monotonic energy-dependent
factor. In these circumstances, it is shown that a maximum time resolution
emerges non-perturbatively only if the total energy is bounded. Perturbatively,
however, there always exists a minimum uncertainty in the physical time.Comment: (4 pages, no figures) Accepted for publication in Physical Review
The correction-to-scaling exponent in dilute systems
The leading correction-to-scaling exponent for the three-dimensional
dilute Ising model is calculated in the framework of the field theoretic
renormalization group approach. Both in the minimal subtraction scheme as well
as in the massive field theory (resummed four loop expansion) excellent
agreement with recent Monte Carlo calculations [Ballesteros H G, et al Phys.
Rev. B 58, 2740 (1998)] is achieved. The expression of as series in a
-expansion up to does not allow a
reliable estimate for .Comment: 4 pages, latex, 1 eps-figure include
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