665 research outputs found
Large-Order Behavior of Two-coupling Constant -Theory with Cubic Anisotropy
For the anisotropic [u (\sum_{i=1^N {\phi}_i^2)^2+v \sum_{i=1^N
\phi_i^4]-theory with {} we calculate the imaginary parts of the
renormalization-group functions in the form of a series expansion in , i.e.,
around the isotropic case. Dimensional regularization is used to evaluate the
fluctuation determinants for the isotropic instanton near the space dimension
4. The vertex functions in the presence of instantons are renormalized with the
help of a nonperturbative procedure introduced for the simple g{\phi^4-theory
by McKane et al.Comment: LaTeX file with eps files in src. See also
http://www.physik.fu-berlin.de/~kleinert/institution.htm
New approach to Borel summation of divergent series and critical exponent estimates for an N-vector cubic model in three dimensions from five-loop \epsilon expansions
A new approach to summation of divergent field-theoretical series is
suggested. It is based on the Borel transformation combined with a conformal
mapping and does not imply the exact asymptotic parameters to be known. The
method is tested on functions expanded in their asymptotic power series. It is
applied to estimating the critical exponent values for an N-vector field model,
describing magnetic and structural phase transitions in cubic and tetragonal
crystals, from five-loop \epsilon expansions.Comment: 9 pages, LaTeX, 3 PostScript figure
Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time Dynamics Study
The short-time dynamic evolution of an Ising model embedded in an infinitely
ramified fractal structure with noninteger Hausdorff dimension was studied
using Monte Carlo simulations. Completely ordered and disordered spin
configurations were used as initial states for the dynamic simulations. In both
cases, the evolution of the physical observables follows a power-law behavior.
Based on this fact, the complete set of critical exponents characteristic of a
second-order phase transition was evaluated. Also, the dynamic exponent of the critical initial increase in magnetization, as well as the critical
temperature, were computed. The exponent exhibits a weak dependence
on the initial (small) magnetization. On the other hand, the dynamic exponent
shows a systematic decrease when the segmentation step is increased, i.e.,
when the system size becomes larger. Our results suggest that the effective
noninteger dimension for the second-order phase transition is noticeably
smaller than the Hausdorff dimension. Even when the behavior of the
magnetization (in the case of the ordered initial state) and the
autocorrelation (in the case of the disordered initial state) with time are
very well fitted by power laws, the precision of our simulations allows us to
detect the presence of a soft oscillation of the same type in both magnitudes
that we attribute to the topological details of the generating cell at any
scale.Comment: 10 figures, 4 tables and 14 page
Structures, origin and evolution of various carbon phases in the ureilite Northwest Africa 4742 compared with laboratory-shocked graphite
International audienceMineralogical structures of carbon phases within the ureilite North West Africa 4742, a recent find, are investigated at various scales by high-resolution transmission electron microscopy (HRTEM), Raman microspectrometry and X-ray diffraction. Ureilites are the most carbon-rich of all meteorites, containing up to 6 wt.% carbon. Diamond, graphite and so-called "amorphous carbon" are typically described, but their crystallographic relationships and respective thermal histories remain poorly constrained. We especially focus on the origin of "amorphous carbon" and graphite, as well as their relationship with diamond. Two aliquots of carbon-bearing material were extracted: the insoluble organic matter (IOM) and the diamond fraction. We also compare the observed structures with those of laboratory-shocked graphite. Polycrystalline diamond aggregates with mean coherent domains of about 40 nm are reported for the first time in a ureilite and TEM demonstrates that all carbon phases are crystallographically related at the nanometre scale. Shock features show that diamond is produced from graphite through a martensitic transition. This observation demonstrates that graphite was present when the shock occurred and is consequently a precursor of diamond. The structure of what is commonly described as the "amorphous carbon" has been identified. It is not completely amorphous but only disordered and consists of nanometre-sized polyaromatic units surrounding the diamond. Comparison with laboratory-shocked graphite, partially transformed into diamond, indicates that the disordered carbon could be the product of diamond post-shock annealing. As diamond is the carrier of noble gases, whereas graphite is noble gas free, graphite cannot be the sole diamond precursor. This implies a multiple-stage history. A first generation of diamond could have been synthesized from a noble gas rich precursor or environment by either a shock or a condensation process. Thermally-induced graphitization of chondritic-like organic matter could have produced the graphite, which was then transformed by shock processes into polycrystalline nanodiamond aggregates. The formation of the disordered carbon occurred by diamond post-shock back-transformation during post-shock heating. The noble gases in the first generation diamond could then be incorporated directly into the disordered carbon during the transformation
Pseudo-epsilon expansion and the two-dimensional Ising model
Starting from the five-loop renormalization-group expansions for the
two-dimensional Euclidean scalar \phi^4 field theory (field-theoretical version
of two-dimensional Ising model), pseudo-\epsilon expansions for the Wilson
fixed point coordinate g*, critical exponents, and the sextic effective
coupling constant g_6 are obtained. Pseudo-\epsilon expansions for g*, inverse
susceptibility exponent \gamma, and g_6 are found to possess a remarkable
property - higher-order terms in these expansions turn out to be so small that
accurate enough numerical estimates can be obtained using simple Pade
approximants, i. e. without addressing resummation procedures based upon the
Borel transformation.Comment: 4 pages, 4 tables, few misprints avoide
The Magnetization of the 3D Ising Model
We present highly accurate Monte Carlo results for simple cubic Ising
lattices containing up to spins. These results were obtained by means
of the Cluster Processor, a newly built special-purpose computer for the Wolff
cluster simulation of the 3D Ising model. We find that the magnetization
is perfectly described by , where
, in a wide temperature range .
If there exist corrections to scaling with higher powers of , they are very
small. The magnetization exponent is determined as (6). An
analysis of the magnetization distribution near criticality yields a new
determination of the critical point: ,
with a standard deviation of .Comment: 7 pages, 5 Postscript figure
Topological and Universal Aspects of Bosonized Interacting Fermionic Systems in (2+1)d
General results on the structure of the bosonization of fermionic systems in
d are obtained. In particular, the universal character of the bosonized
topological current is established and applied to generic fermionic current
interactions. The final form of the bosonized action is shown to be given by
the sum of two terms. The first one corresponds to the bosonization of the free
fermionic action and turns out to be cast in the form of a pure Chern-Simons
term, up to a suitable nonlinear field redefinition. We show that the second
term, following from the bosonization of the interactions, can be obtained by
simply replacing the fermionic current by the corresponding bosonized
expression.Comment: 29 pages, RevTe
Critical exponents for 3D O(n)-symmetric model with n > 3
Critical exponents for the 3D O(n)-symmetric model with n > 3 are estimated
on the base of six-loop renormalization-group (RG) expansions. A simple
Pade-Borel technique is used for the resummation of the RG series and the Pade
approximants [L/1] are shown to give rather good numerical results for all
calculated quantities. For large n, the fixed point location g_c and the
critical exponents are also determined directly from six-loop expansions
without addressing the resummation procedure. An analysis of the numbers
obtained shows that resummation becomes unnecessary when n exceeds 28 provided
an accuracy of about 0.01 is adopted as satisfactory for g_c and critical
exponents. Further, results of the calculations performed are used to estimate
the numerical accuracy of the 1/n-expansion. The same value n = 28 is shown to
play the role of the lower boundary of the domain where this approximation
provides high-precision estimates for the critical exponents.Comment: 10 pages, TeX, no figure
The DICE calibration project: design, characterization, and first results
We describe the design, operation, and first results of a photometric
calibration project, called DICE (Direct Illumination Calibration Experiment),
aiming at achieving precise instrumental calibration of optical telescopes. The
heart of DICE is an illumination device composed of 24 narrow-spectrum,
high-intensity, light-emitting diodes (LED) chosen to cover the
ultraviolet-to-near-infrared spectral range. It implements a point-like source
placed at a finite distance from the telescope entrance pupil, yielding a flat
field illumination that covers the entire field of view of the imager. The
purpose of this system is to perform a lightweight routine monitoring of the
imager passbands with a precision better than 5 per-mil on the relative
passband normalisations and about 3{\AA} on the filter cutoff positions. The
light source is calibrated on a spectrophotometric bench. As our fundamental
metrology standard, we use a photodiode calibrated at NIST. The radiant
intensity of each beam is mapped, and spectra are measured for each LED. All
measurements are conducted at temperatures ranging from 0{\deg}C to 25{\deg}C
in order to study the temperature dependence of the system. The photometric and
spectroscopic measurements are combined into a model that predicts the spectral
intensity of the source as a function of temperature. We find that the
calibration beams are stable at the level -- after taking the slight
temperature dependence of the LED emission properties into account. We show
that the spectral intensity of the source can be characterised with a precision
of 3{\AA} in wavelength. In flux, we reach an accuracy of about 0.2-0.5%
depending on how we understand the off-diagonal terms of the error budget
affecting the calibration of the NIST photodiode. With a routine 60-mn
calibration program, the apparatus is able to constrain the passbands at the
targeted precision levels.Comment: 25 pages, 27 figures, accepted for publication in A&
Large-N expansion based on the Hubbard-operator path integral representation and its application to the model
In the present work we have developed a large-N expansion for the model
based on the path integral formulation for Hubbard-operators. Our large-N
expansion formulation contains diagrammatic rules, in which the propagators and
vertex are written in term of Hubbard operators. Using our large-N formulation
we have calculated, for J=0, the renormalized boson propagator. We
also have calculated the spin-spin and charge-charge correlation functions to
leading order 1/N. We have compared our diagram technique and results with the
existing ones in the literature.Comment: 6 pages, 3 figures, Phys.Rev.B (in press
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