Critical behavior and propagator-dependent energy functional in a scalar field model

In this paper, we calculate the vacuum energy as a functional from the phion propagator in 4D model of complex scalar field (phion) which interacts with a real matrix scalar field (chion). The condition of stationarity of this functional gives us the equation for phion propagator. At some critical value of the coupling, the propagator changes its asymptotic behavior in the deep-Euclidean region of momenta. This behavior corresponds to some critical phenomenon. The study of the convexity of the energy functional shows that the solution obtained actually corresponds to the theory. We also discuss the stabilization of the ground state in the strong-coupling region by effective self-action of phions.