  The spontaneous symmetry breaking at zero temperature in the four-component
four-dimensional scalar $\lambda \phi^4_4$ model (the O(4) model) is
investigated on a lattice for different values of the coupling constant
$\lambda$. A general method for dealing with such type dependence is developed.
The Goldstone modes are integrated out in the spherical coordinates in the
internal space of the scalar field by the saddle point method, and the initial
functional integral of the model is reduced to an effective one-component
theory convenient for lattice investigations. The partition function of this
theory is calculated analytically in the static limit and demonstrates the
$\lambda$-dependence which is characteristic for distinguishing symmetry
breaking. Monte Carlo simulations are performed with the QCDGPU software
package on a HGPU cluster. It is shown that the symmetry is spontaneously
broken for $\lambda>\lambda_0 \simeq 10^{-5}$. For smaller coupling values, the
scalar field vanishes on a lattice, which can be interpreted as instability of
the homogeneous condensate or even instability of the model itself. The
critical value $\lambda_0$ is independent of the lattice sizes $16^4$ and
$32^4$ investigated.
