Asymptotic behavior and critical coupling in scalar Yukawa model

The solution of the equation for the phion propagator in the leading order of the $1\mathrm{/}N$ – expansion for a vector-matrix model with interaction $g({\varphi }_a{)}^{\ast }{\varphi }_b{\chi }_{ab}$ in four dimensions shows a change of the asymptotic behavior in the deep Euclidean region in a vicinity of a certain critical value of the coupling constant.