Decoupling Transformations in Path Integral Bosonization

We construct transformations that decouple fermionic fields in interaction with a gauge field, in the path integral representation of the generating functional. Those transformations express the original fermionic fields in terms of non-interacting ones, through non-local functionals depending on the gauge field. This procedure, holding true in any number of spacetime dimensions both in the Abelian and non-Abelian cases, is then applied to the path integral bosonization of the Thirring model in 3 dimensions. Knowledge of the decoupling transformations allows us, contrarily to previous bosonizations, to obtain the bosonization with an explicit expression of the fermion fields in terms of bosonic ones and free fermionic fields. We also explain the relation between our technique, in the two dimensional case, and the usual decoupling in 2 dimensions.Comment: 22 pages, Late

Large-Order Behavior of Two-coupling Constant ϕ4\phi^4-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 {$N=2,3$} we calculate the imaginary parts of the renormalization-group functions in the form of a series expansion in $v$, 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

Five-loop additive renormalization in the phi^4 theory and amplitude functions of the minimally renormalized specific heat in three dimensions

We present an analytic five-loop calculation for the additive renormalization constant A(u,epsilon) and the associated renormalization-group function B(u) of the specific heat of the O(n) symmetric phi^4 theory within the minimal subtraction scheme. We show that this calculation does not require new five-loop integrations but can be performed on the basis of the previous five-loop calculation of the four-point vertex function combined with an appropriate identification of symmetry factors of vacuum diagrams. We also determine the amplitude functions of the specific heat in three dimensions for n=1,2,3 above T_c and for n=1 below T_c up to five-loop order. Accurate results are obtained from Borel resummations of B(u) for n=1,2,3 and of the amplitude functions for n=1. Previous conjectures regarding the smallness of the resummed higher-order contributions are confirmed. Borel resummed universal amplitude ratios A^+/A^- and a_c^+/a_c^- are calculated for n=1.Comment: 30 pages REVTeX, 3 PostScript figures, submitted to Phys. Rev.

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

Critical Exponents of the N-vector model

Recently the series for two RG functions (corresponding to the anomalous dimensions of the fields phi and phi^2) of the 3D phi^4 field theory have been extended to next order (seven loops) by Murray and Nickel. We examine here the influence of these additional terms on the estimates of critical exponents of the N-vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within errors of the previous evaluation. Exponents like eta (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou--Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published epsilon=4-d expansions (order epsilon^5), we have also reanalyzed the determination of exponents from the epsilon-expansion. The conclusion is that the general agreement between epsilon-expansion and 3D series has improved with respect to Le Guillou--Zinn-Justin.Comment: TeX Files, 27 pages +2 figures; Some values are changed; references update

Quantum Bubble Nucleation beyond WKB: Resummation of Vacuum Bubble Diagrams

On the basis of Borel resummation, we propose a systematical improvement of bounce calculus of quantum bubble nucleation rate. We study a metastable super-renormalizable field theory, $D$ dimensional O(N) symmetric $\phi^4$ model ($D<4$) with an attractive interaction. The validity of our proposal is tested in D=1 (quantum mechanics) by using the perturbation series of ground state energy to high orders. We also present a result in D=2, based on an explicit calculation of vacuum bubble diagrams to five loop orders.Comment: 19 pages, 5 figures, PHYZZ

A new improved optimization of perturbation theory: applications to the oscillator energy levels and Bose-Einstein critical temperature

Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method which leads to a drastic reduction of the number of acceptable solutions. The properties of this new method are studied and it is then applied to the calculation of relevant quantities in different $\phi^4$ models, such as the anharmonic oscillator energy levels and the critical Bose-Einstein Condensation temperature shift $\Delta T_c$ recently investigated by various authors. Our present estimates of $\Delta T_c$, incorporating the most recently available six and seven loop perturbative information, are in excellent agreement with all the available lattice numerical simulations. This represents a very substantial improvement over previous treatments.Comment: 9 pages, no figures. v2: minor wording changes in title/abstract, to appear in Phys.Rev.

The Magnetization of the 3D Ising Model

We present highly accurate Monte Carlo results for simple cubic Ising lattices containing up to $256^3$ 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 $M(t)$ is perfectly described by $M(t)=(a_0-a_1 t^{\theta} - a_2 t) t^{\beta}$, where $t=(T_{\rm c}-T)/T_{\rm c}$, in a wide temperature range $0.0005 < t < 0.26$. If there exist corrections to scaling with higher powers of $t$, they are very small. The magnetization exponent is determined as $\beta=0.3269$ (6). An analysis of the magnetization distribution near criticality yields a new determination of the critical point: $K_{\rm c}=J/k_B T_{\rm c}=0.2216544$, with a standard deviation of $3\cdot 10^{-7}$.Comment: 7 pages, 5 Postscript figure

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