Some recent contributions to Geography

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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 $N$. The critical dimensionality $N_c=2.89 \pm 0.02$ and the stability matrix eigenvalues estimates obtained on the basis of the generalized Pad$\acute{\rm e}$-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 $\omega$ 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 $\omega$ as series in a $\sqrt{\epsilon}$-expansion up to ${\cal O}(\epsilon^2)$ does not allow a reliable estimate for $d=3$.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 $N$ up to the four-loop order and resummed by means of the generalized Pad$\acute{\rm e}$-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 $N_c=2.89 \pm 0.02$ 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 $N\ge3$, 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 ϵ1/2\epsilon^{1/2}-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 $\phi^4$-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 $\epsilon^{1/2}$-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. $\epsilon^{1/2}$-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