Diagram technique for the low-temperature phase in the chiral field model

A perturbation theory in powers of $1/N$ is constructed for the lower phase of the threedimensional chiral field model. The diagrams have the peculiar property that although they contain $N$ propagators of the massless field the model contains only $N-1$ Goldstone particles and the $O(N)$ symmetry is broken. The constructed $1/N$ perturbation theory for the lower phase is renormalizable and free of infrared divergences. It is shown that for the lower phase a Wilson expansion of special form is valid: $(n(x),n(x+\varepsilon))=C(\varepsilon)+R(x,\varepsilon)$, where $C(\varepsilon)$ is a $c$-number and $R(x,e)$ converges weakly to zero as $\varepsilon\to\infty$.