  We have extended our method of grouping of Feynman diagrams (GFD theory) to
study the transverse (G_t) and longitudinal (G_l) Greens functions in phi^4
model below the critical point (T<T_c) in presence of an infinitesimal external
field. Our method allows a qualitative analysis not cutting the perturbation
series. We have shown that the critical behavior of the Greens (correlation)
functions is consistent with a general scaling hypothesis, where the same
critical exponents, found within the GFD theory, are valid both at T<T_c and
T>T_c. The long-wave limit k->0 has been studied at T<T_c, showing that the
transverse and the longitudinal correlation functions diverge as 1/k in the
power of lambda_t and lambda_l, respectively, where d/2< lambda_t < 2 and
lambda_l = 2 lambda_t - d holds at the spatial dimensionality 2<d<4. It is the
physical solution of our equations, which coincides with the asymptotic
solution at T -> T_c as well as with a non-perturbative renormalization group
(RG) analysis provided in our paper. It is confirmed also by Monte Carlo
simulation. The exponents, as well as the ratio bM^2/a^2 (where M is
magnetization, a and b are the amplitudes of G_t and G_l at k->0) are
universal. The results of the perturbative RG method are reproduced by formally
setting lambda_t=2. Nevertheless, we disprove the conventional statement that
lambda_t=2 is the exact result.
