In this paper, we study O(2N)-symmetric $ϕ^4$-theory at finite temperature and density using the 2PI-1/N expansion. As specific examples, we consider pion condensation at finite isospin chemical potential and kaon condensation at finite chemical potential for hyper charge and isospin charge. We calculate the phase diagrams and the quasiparticle masses for pions and kaons in the large-N limit. It is shown that the effective potential and the gap equation can be renormalized by using local counterterms for the coupling constant and mass parameter, which are independent of temperature and chemical potentials.

10 pages. 7 Figures. v2: Better plots and figs. Added significant number of refs v3: Accepted for publication in PRD. Added a figure and improved part on renormalization as well as presentation