Stability of 3D Cubic Fixed Point in Two-Coupling-Constant \phi^4-Theory

For an anisotropic euclidean $\phi^4$-theory with two interactions [u (\sum_{i=1^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4] the $\beta$-functions are calculated from five-loop perturbation expansions in $d=4-\varepsilon$ dimensions, using the knowledge of the large-order behavior and Borel transformations. For $\varepsilon=1$, an infrared stable cubic fixed point for $M \geq 3$ is found, implying that the critical exponents in the magnetic phase transition of real crystals are of the cubic universality class. There were previous indications of the stability based either on lower-loop expansions or on less reliable Pad\'{e approximations, but only the evidence presented in this work seems to be sufficently convincing to draw this conclusion.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re250/preprint.htm

Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length

We extend previous work on applying the epsilon-expansion to universal properties of a cold, dilute Fermi gas in the unitary regime of infinite scattering length. We compute the ratio xi = mu/epsilon_F of chemical potential to ideal gas Fermi energy to next-to-next-to-leading order (NNLO) in epsilon=4-d, where d is the number of spatial dimensions. We also explore the nature of corrections from the order after NNLO.Comment: 28 pages, 14 figure

Obtaining Bounds on The Sum of Divergent Series in Physics

Under certain circumstances, some of which are made explicit here, one can deduce bounds on the full sum of a perturbation series of a physical quantity by using a variational Borel map on the partial series. The method is illustrated by applying it to various examples, physical and mathematical.Comment: 33 pages, Journal Versio

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

Interpolation Parameter and Expansion for the Three Dimensional Non-Trivial Scalar Infrared Fixed Point

We compute the non--trivial infrared $\phi^4_3$--fixed point by means of an interpolation expansion in fixed dimension. The expansion is formulated for an infinitesimal momentum space renormalization group. We choose a coordinate representation for the fixed point interaction in derivative expansion, and compute its coordinates to high orders by means of computer algebra. We compute the series for the critical exponent $\nu$ up to order twenty five of interpolation expansion in this representation, and evaluate it using \pade, Borel--\pade, Borel--conformal--\pade, and Dlog--\pade resummation. The resummation returns $0.6262(13)$ as the value of $\nu$.Comment: 29 pages, Latex2e, 2 Postscript figure

Duality between Topologically Massive and Self-Dual models

We show that, with the help of a general BRST symmetry, different theories in 3 dimensions can be connected through a fundamental topological field theory related to the classical limit of the Chern-Simons model.Comment: 13 pages, LaTe

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