Self-consistent treatment of a phase transition in a system with a vector order parameter

The problem of the continuation of the Hartree approximation below the transition temperature is considered for a system with a vector order parameter, In contrast to the case of a scalar order parameter, considered in a previous paper, it is found that a self-consistent and gapless approximation can be constructed in the limit of a very large number of vector components. The results agree with those of the spherical model.