  The Ginzburg-Landau phase transition model is considered in d=4-epsilon
dimensions within the renormalization group (RG) approach. The problem of
existence of the non-Gaussian fixed point is discussed. An equation is derived
from the first principles of the RG theory (under the assumption that the fixed
point exists) for calculation of the correction-to-scaling term in the
asymptotic expansion of the two-point correlation (Green's) function. It is
demonstrated clearly that, within the framework of the standard methods (well
justified in the vicinity of the fixed point) used in the perturbative RG
theory, this equation leads to an unremovable contradiction with the known RG
results. Thus, in its very basics, the RG field theory in 4-epsilon dimensions
is contradictory. To avoid the contradiction, we conclude that such a
non-Gaussian fixed point, as predicted by the RG field theory, does not exist.
Our consideration does not exclude existence of a different fixed point.
