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

摘要

For an O(N)-symmetric scalar field theory with Euclidean action integrald(3) x[1/2delphi/(2) + 1/2 + rphi(2)+1/4! uphi(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 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 The Appendix contains previously unpublished numerical seven-loop data.