Counterterm resummation for 2PI-approximation in constant background

Explicit counterterm construction is presented in a symmetry breaking background for the 2PI effective action of the self-interacting one-component scalar field including skeleton diagrams to O(λ2). The applied strategy is an extension of our treatment of the 2PI-Hartree approximation [G. Fejős, A. Patkós, Zs. Szép, Nucl. Phys. A 803 (2008) 135, arXiv: 0711.2933]. The procedure is also applied to the O(N) model.