  We apply a truncated set of dynamical equations of motion for connected
equal-time Green functions up to the 4-point level to the investigation of
spontaneous ground state symmetry breaking in $\Phi^4_{2+1}$ quantum field
theory. Within our momentum space discretization we obtain a second order phase
transition as soon as the connected 3-point function is included. However, an
additional inclusion of the connected 4-point function still shows a
significant influence on the shape of the effective potential and the critical
coupling.
