  The system of two scalar order parameters on a complex scale-free network is
analyzed in the spirit of Landau theory. To add a microscopic background to the
phenomenological approach we also study a particular spin Hamiltonian that
leads to coupled scalar order behavior using the mean field approximation. Our
results show that the system is characterized by either of two types of
ordering: either one of the two order parameters is zero or both are non-zero
but have the same value. While the critical exponents do not differ from those
of a model with a single order parameter on a scale free network there are
notable differences for the amplitude ratios and susceptibilities. Another
peculiarity of the model is that the transverse susceptibility is divergent at
all T<T_c, when O(n) symmetry is present. This behavior is related to the
appearance of Goldstone modes.
