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

Abstract

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<phi^2>/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 The appendix contains previously unpublished numerical seven-loop data provided to us by B.Nickel.

19 pages

References in corpus (26)

• Critical Phenomena and Renormalization-Group Theory
• Theory of the Weakly Interacting Bose Gas
• Worm algorithms for classical statistical models
• Condensate fraction and critical temperature of a trapped interacting Bose gas
• The transition temperature of the dilute interacting Bose gas
• Transition temperature of a dilute homogeneous imperfect Bose gas
• Seven-Loop Critical Exponents from Strong-Coupling phi^4-Theory in Three Dimensions
• The transition temperature of the dilute interacting Bose gas for $N$ internal degrees of freedom
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops
• T_c for dilute Bose gases: beyond leading order in 1/N
• Addendum to paper: Strong-Coupling Behavior of ${\varphi }^4$-Theories and Critical Exponents [Phys. Rev. D 57, 2264 (1998)]
• Monte Carlo simulation of O(2) phi^4 field theory in three dimensions
• T_c for homogeneous dilute Bose gases: a second-order result
• Non-analytic dependence of the transition temperature of the homogeneous dilute Bose gas on scattering length
• T_c for trapped dilute Bose gases: a second-order result
• A new improved optimization of perturbation theory: applications to the oscillator energy levels and Bose-Einstein critical temperature
• Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops
• Recursive Graphical Construction of Feynman Diagrams and Their Multiplicities in phi^4- and in phi^2A-Theory
• Monte Carlo studies of three-dimensional O(1) and O(4) \boldmath{${\varphi }^4$} theory related to BEC phase transition temperatures
• Variational Interpolation Algorithm between Weak- and Strong-Coupling Expansions
• Theory and Satellite Experiment for Critical Exponent alpha of lambda-Transition in Superfluid Helium
• Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory
• Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory
• Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy
• Shift of BEC Temperature of Homogenous Weakly Interacting Bose Gas

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