Nonuniversal critical quantities from variational perturbation theory and their application to the Bose-Einstein condensation temperature shift

Boris Kastening
Phys. Rev. A 70, 043621 – Published 20 October 2004

Abstract

For an O(N)-symmetric scalar field theory with Euclidean action d3x[12ϕ2+12rϕ2+14!uϕ4], where ϕ=(ϕ1,,ϕN) 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)u2 at the phase transition. Its exact large-N limit is determined as well. We also extend an earlier computation of the interaction-induced shift Δϕ2Nu from 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 The Appendix contains previously unpublished numerical seven-loop data.

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  • Received 7 June 2004

DOI:https://doi.org/10.1103/PhysRevA.70.043621

©2004 American Physical Society

Authors & Affiliations

Boris Kastening*

  • Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany

  • *Electronic address: boris.kastening@physik.fu-berlin.de

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Vol. 70, Iss. 4 — October 2004

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