3,510 research outputs found
The stability of a cubic fixed point in three dimensions from the renormalization group
The global structure of the renormalization-group flows of a model with
isotropic and cubic interactions is studied using the massive field theory
directly in three dimensions. The four-loop expansions of the \bt-functions
are calculated for arbitrary . The critical dimensionality and the stability matrix eigenvalues estimates obtained on the basis of
the generalized Pad-Borel-Leroy resummation technique are shown
to be in a good agreement with those found recently by exploiting the five-loop
\ve-expansions.Comment: 18 pages, LaTeX, 5 PostScript figure
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
Dressing the nucleon in a dispersion approach
We present a model for dressing the nucleon propagator and vertices. In the
model the use of a K-matrix approach (unitarity) and dispersion relations
(analyticity) are combined. The principal application of the model lies in
pion-nucleon scattering where we discuss effects of the dressing on the phase
shifts.Comment: 17 pages, using REVTeX, 6 figure
Compton scattering on the nucleon at intermediate energies and polarizabilities in a microscopic model
A microscopic calculation of Compton scattering on the nucleon is presented
which encompasses the lowest energies -- yielding nucleon polarizabilities --
and extends to energies of the order of 600 MeV. We have used the covariant
"Dressed K-Matrix Model" obeying the symmetry properties which are appropriate
in the different energy regimes. In particular, crossing symmetry, gauge
invariance and unitarity are satisfied. The extent of violation of analyticity
(causality) is used as an expansion parameter.Comment: 35 pages, 15 figures, using REVTeX. Modified version to be published
in Phys. Rev. C, more extensive comparison with data for Compton scattering,
all results unchange
Stability of a cubic fixed point in three dimensions. Critical exponents for generic N
The detailed analysis of the global structure of the renormalization-group
(RG) flow diagram for a model with isotropic and cubic interactions is carried
out in the framework of the massive field theory directly in three dimensions
(3D) within an assumption of isotropic exchange. Perturbative expansions for RG
functions are calculated for arbitrary up to the four-loop order and
resummed by means of the generalized Pad-Borel-Leroy technique.
Coordinates and stability matrix eigenvalues for the cubic fixed point are
found under the optimal value of the transformation parameter. Critical
dimensionality of the model is proved to be equal to that
agrees well with the estimate obtained on the basis of the five-loop
\ve-expansion [H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B342, 284
(1995)] resummed by the above method. As a consequence, the cubic fixed point
should be stable in 3D for , and the critical exponents controlling
phase transitions in three-dimensional magnets should belong to the cubic
universality class. The critical behavior of the random Ising model being the
nontrivial particular case of the cubic model when N=0 is also investigated.
For all physical quantities of interest the most accurate numerical estimates
with their error bounds are obtained. The results achieved in the work are
discussed along with the predictions given by other theoretical approaches and
experimental data.Comment: 33 pages, LaTeX, 7 PostScript figures. Final version corrected and
added with an Appendix on the six-loop stud
Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus -Expansion
We present a field-theoretical treatment of the critical behavior of
three-dimensional weakly diluted quenched Ising model. To this end we analyse
in a replica limit n=0 5-loop renormalization group functions of the
-theory with O(n)-symmetric and cubic interactions (H.Kleinert and
V.Schulte-Frohlinde, Phys.Lett. B342, 284 (1995)). The minimal subtraction
scheme allows to develop either the -expansion series or to
proceed in the 3d approach, performing expansions in terms of renormalized
couplings. Doing so, we compare both perturbation approaches and discuss their
convergence and possible Borel summability. To study the crossover effect we
calculate the effective critical exponents providing a local measure for the
degree of singularity of different physical quantities in the critical region.
We report resummed numerical values for the effective and asymptotic critical
exponents. Obtained within the 3d approach results agree pretty well with
recent Monte Carlo simulations. -expansion does not allow
reliable estimates for d=3.Comment: 35 pages, Latex, 9 eps-figures included. The reference list is
refreshed and typos are corrected in the 2nd versio
Divergent Perturbation Series
Various perturbation series are factorially divergent. The behavior of their
high-order terms can be found by Lipatov's method, according to which they are
determined by the saddle-point configurations (instantons) of appropriate
functional integrals. When the Lipatov asymptotics is known and several lowest
order terms of the perturbation series are found by direct calculation of
diagrams, one can gain insight into the behavior of the remaining terms of the
series. Summing it, one can solve (in a certain approximation) various
strong-coupling problems. This approach is demonstrated by determining the
Gell-Mann - Low functions in \phi^4 theory, QED, and QCD for arbitrary coupling
constants. An overview of the mathematical theory of divergent series is
presented, and interpretation of perturbation series is discussed. Explicit
derivations of the Lipatov asymptotic forms are presented for some basic
problems in theoretical physics. A solution is proposed to the problem of
renormalon contributions, which hampered progress in this field in the late
1970s. Practical schemes for summation of perturbation series are described for
a coupling constant of order unity and in the strong-coupling limit. An
interpretation of the Borel integral is given for 'non-Borel-summable' series.
High-order corrections to the Lipatov asymptotics are discussed.Comment: Review article, 45 pages, PD
Obesity control by SHIP inhibition requires pan-paralog inhibition and an intact eosinophil compartment
peer reviewedHere we extend the understanding of how chemical inhibition of SHIP paralogs controls obesity. We compare different classes of SHIP inhibitors and find that selective inhibitors of SHIP1 or SHIP2 are unable to prevent weight gain and body fat accumulation during increased caloric intake. Surprisingly, only pan-SHIP1/2 inhibitors (pan-SHIPi) prevent diet-induced obesity. We confirm that pan-SHIPi is essential by showing that dual treatment with SHIP1 and SHIP2 selective inhibitors reduced adiposity during excess caloric intake. Consistent with this, genetic inactivation of both SHIP paralogs in eosinophils or myeloid cells also reduces obesity and adiposity. In fact, pan-SHIPi requires an eosinophil compartment to prevent diet-induced adiposity, demonstrating that pan-SHIPi acts via an immune mechanism. We also find that pan-SHIPi increases ILC2 cell function in aged, obese mice to reduce their obesity. Finally, we show that pan-SHIPi also reduces hyperglycemia, but not via eosinophils, indicating a separate mechanism for glucose control
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