2004/06/01 by Boris Kastening
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #Quantum, superfluid, helium dynamics #cond-mat.stat-mech #hep-ph
paper · pdf · doi:10.1103/physreva.70.043621
published as Phys. Rev. A 70, 043621 (2004) · 19 pages
arxiv created 2004/06/01 · openalex publication_date 2004/10/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
For an O(N)-symmetric scalar field theory with Euclidean action \ensuremath∫d3\phantom\rule0.3em0exx[(1)/(2)\ensuremath|\ensuremath∇\ensuremathφ\ensuremath|2+(1)/(2)r\ensuremathφ2+(1)/(4!)u\ensuremathφ4], where \ensuremathφ=(\ensuremathφ1,…,\ensuremathφN) 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 \ensuremathΔ⟨\ensuremathφ2⟩∕Nu 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 The Appendix contains previously unpublished numerical seven-loop data.