Asymptotic behavior in the scalar field theory

An asymptotic solution of the system of Schwinger-Dyson equations for four-dimensional Euclidean scalar field theory with interaction $\frac{\lambda }{2}({\varphi }^{\ast }\varphi {)}^2$ is obtained. For $\lambda >{\lambda }_{cr}=16{\pi }^2$ the two-particle amplitude has the pathology-free asymptotic behavior at large momenta. For $\lambda <{\lambda }_{cr}$ the amplitude possesses Landau-type singularity.