The perturbation expansion and goldstone singularities in the ordered phase of the $O_n$-symmetrical $\mathbf \Phi^4$-theory in half space

The $O_n$-symmetrical $\mathbf \Phi^4$-theory in half space is investigated. Below critical temperature free propagators are obtained in this theory without external field, and their dependence from boundary conditions is studied. The general forms of Goldstone asymptotics of different correlators being functions of small external fields, momenta and large distances from the boundary of the system are determined.