Journal of Statistical Physics, Vol. 30, No. 3, 1983. p. 607-615.
The validity of the vertex approximation for the nonlinear Langevin equations has been investigated in the special case of a two-component magnetic system without spatial correlation. The exact solution of the equation resulting from the vertex approximation is compared with that of the original equation. Agreement is found in the regime of small nonlinearity. In the opposite regime, especially near a critical slowing down, both solutions differ significantly.