Nonuniversal critical quantities from variational perturbation theory and their application to the Bose-Einstein condensation temperature shift
Nonuniversal critical quantities from variational perturbation theory and their application to the Bose-Einstein condensation temperature shift
For an $\mathrm{O}(N)$-symmetric scalar field theory with Euclidean action $\ensuremath{\int}{d}^{3}\phantom{\rule{0.3em}{0ex}}x[\frac{1}{2}\ensuremath{\mid}\ensuremath{\nabla}\ensuremath{\phi}{\ensuremath{\mid}}^{2}+\frac{1}{2}r{\ensuremath{\phi}}^{2}+\frac{1}{4!}u{\ensuremath{\phi}}^{4}]$, where $\ensuremath{\phi}=({\ensuremath{\phi}}_{1},\dots{},{\ensuremath{\phi}}_{N})$ 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 …