Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase

Non-perturbative renormalisation of a general class of scalar field theories is performed at the Hartree level truncation of the 2PI effective action in the broken symmetry regime. Renormalised equations are explicitly constructed for the one- and two-point functions. The non-perturbative counterterms are deduced from the conditions for the cancellation of the overall and the subdivergences in the complete Hartree–Dyson–Schwinger equations, with a transparent method. The procedure proposed in the present paper is shown to be equivalent to the iterative renormalisation method of Blaizot et al. [J.-P. Blaizot, E. Iancu, U. Reinosa, Nucl. Phys. A 736 (2004) 149, hep-ph/0312085].