  We study the $O(4)$-symmetric $ \Phi^4 $-theory in the scaling region of the
broken phase using the standard and a Symanzik improved action with infinite
bare self-coupling $\lambda$. A high precision Monte Carlo simulation is
performed by applying the reflection cluster algorithm. Employing the histogram
method we analytically continue to a sequence of values of the hopping
parameter $\kappa$ neighbouring the actually simulated ones. In the
investigated vicinity of the critical point $\kappa_{c}$ finite volume effects
affecting, e.g., the determination of the field expectation value $\Sigma$ and
the mass $m_\sigma$ of the $\sigma$-particle are very well described by 1-loop
renormalized perturbation theory. We carry out a detailed scaling analysis on a
high level of precision. Finally we discuss the upper bound on the Higgs mass
for both kinds of actions.
