Bounds from Stability and Symmetry Breaking on Parameters in the Two-Higgs-Doublet Potential

The most general $SU(2)\times U(1)_Y$-symmetric quartic potential with two Higgs doublets, subject to an only softly broken discrete symmetry $(\phi_1,\phi_2)\to(-\phi_1,\phi_2)$, is considered. At tree-level, analytic bounds on the parameters are derived that ensure a stable vacuum, breaking $SU(2)\times U(1)_Y$ down to $U(1)_{em}$.Comment: from last year, but due to recent interest now on the e-print archive, 8 pages, no figures, plain late

Universal anisotropic finite-size critical behavior of the two-dimensional Ising model on a strip and of d-dimensional models on films

Anisotropy effects on the finite-size critical behavior of a two-dimensional Ising model on a general triangular lattice in an infinite-strip geometry with periodic, antiperiodic, and free boundary conditions (bc) in the finite direction are investigated. Exact results are obtained for the scaling functions of the finite-size contributions to the free energy density. With xi_> the largest and xi_< the smallest bulk correlation length at a given temperature near criticality, we find that the dependence of these functions on the ratio xi_ and on the angle parameterizing the orientation of the correlation volume is of geometric rather than dynamic origin. Since the scaling functions are independent of the particular microscopic realization of the anisotropy within the two-dimensional Ising model, our results provide a limited verification of universality. We explain our observations by considering finite-size scaling of free energy densities of general weakly anisotropic models on a d-dimensional film, i.e., in an L x infinity^(d-1) geometry, with bc in the finite direction that are invariant under a shear transformation relating the anisotropic and isotropic cases. This allows us to relate free energy scaling functions in the presence of an anisotropy to those of the corresponding isotropic system. We interpret our results as a simple and transparent case of anisotropic universality, where, compared to the isotropic case, scaling functions depend additionally on the shape and orientation of the correlation volume. We conjecture that this universality extends to cases where the geometry and/or the bc are not invariant under the shear transformation and argue in favor of validity of two-scale factor universality for anisotropic systems.Comment: 16 pages, 4 figures; ref. [14] correcte

Perturbative Finite-Temperature Results and Pad'e Approximants

Pad'e approximants are used to improve the convergence behavior of perturbative results in massless scalar and gauge field theories at finite temperature.Comment: 11 pages, LaTeX, incl. 10 ps-figures; typo in caption of fig.4 corrected; to appear in Phys.Rev.

Fluctuation Pressure of a Membrane Between Walls Through Five Loops

An earlier four-loop calculation of the fluctuation pressure of a fluid membrane between two infinite walls is extended to five loops. Variational perturbation theory is used to extract the hard-wall limit from perturbative results obtained with a smooth potential. Comparison with a structurally similar quantum mechanics problem of a particle in a box is used for an alternative way of extracting the membrane pressure and also to estimate the quality of the results. Our values lie above the best available Monte Carlo data.Comment: 18 pages, 3 figures, typos in references fixe

Shift of BEC Temperature of Homogenous Weakly Interacting Bose Gas

We report on the computation of the shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the diluteness parameter a n^(1/3), where `a' is the scattering length and `n' is the particle density. The perturbative series, which is afflicted by infrared divergences, is resummed by means of variational perturbation theory. Using coefficients through seven loops, we arrive at Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3), which compares favorably with recent Monte-Carlo data.Comment: Talk presented at the 12th International Laser Physics Workshop, LPHYS'03 (Hamburg, Germany, August 25-29, 2003

Functional Differential Equations for the Free Energy and the Effective Energy in the Broken-Symmetry Phase of phi^4-Theory and Their Recursive Graphical Solution

Extending recent work on QED and the symmetric phase of the euclidean multicomponent scalar \phi^4-theory, we construct the vacuum diagrams of the free energy and the effective energy in the ordered phase of \phi^4-theory. By regarding them as functionals of the free correlation function and the interaction vertices, we graphically solve nonlinear functional differential equations, obtaining loop by loop all connected and one-particle irreducible vacuum diagrams with their proper weights.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/31

Non-universal Critical Quantities from Variational Perturbation Theory and Their Application to the BEC Temperature Shift

For an O(N) symmetric scalar field theory with Euclidean action integral d^3x [1/2 |nabla phi|^2 + 1/2 r phi^2 + 1/4! u phi^4], where phi = (phi_1,...,phi_N) is a vector of N real field components, variational perturbation theory through seven loops is employed for N = 0,1,2,3,4 to compute the renormalized value of r/(N+2)u^2 at the phase transition. Its exact large-N limit is determined as well. We also extend an earlier computation of the interaction-induced shift Delta/Nu for N = 1,2,4 to N = 0,3. For N = 2, the results for the two quantities are used to compute the second-order shift of the condensation temperature of a dilute Bose gas, both in the homogenous case and for the wide limit of a harmonic trap. Our results are in agreement with earlier Monte Carlo simulations for N = 1,2,4. The appendix contains previously unpublished numerical seven-loop data provided to us by B.Nickel.Comment: 19 page

Four-Loop Vacuum Energy Beta Function in O(N) Symmetric Scalar Theory

The beta function of the vacuum energy density is computed at the four-loop level in massive O(N) symmetric phi^4 theory. Dimensional regularization is used in conjunction with the MSbar scheme and all calculations are in momentum space in the massive theory. The result is beta_v = g N/4+g^3 N(N+2)/96+g^4 N(N+2)(N+8)[12 zeta(3)-25]/1296+o(g^5).Comment: 16 pages, latex, no figures. Enlarged and updated reference list, minor typographical change

Efficient Algorithm for Perturbative Calculation of Multiloop Feynman Integrals

We present an efficient algorithm for calculating multiloop Feynman integrals perturbatively.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/29

Simplified Transfer Matrix Approach in the Two-Dimensional Ising Model with Various Boundary Conditions

A recent simplified transfer matrix solution of the two-dimensional Ising model on a square lattice with periodic boundary conditions is generalized to periodic-antiperiodic, antiperiodic-periodic and antiperiodic-antiperiodic boundary conditions. It is suggested to employ linear combinations of the resulting partition functions to investigate finite-size scaling. An exact relation of such a combination to the partition function corresponding to Brascamp-Kunz boundary conditions is found.Comment: Phys.Rev.E, to be publishe