  In three-dimensional O(N) models, we investigate the low-momentum behavior of
the two-point Green's function G(x) in the critical region of the symmetric
phase. We consider physical systems whose criticality is characterized by a a
rotationally-invariant fixed point.
  In non rotationally-invariant physical systems with O(N)-invariant
interactions, the vanishing of anisotropy in approaching the
rotationally-invariant fixed point is described by a critical exponent rho,
which is universal and is related to the leading irrelevant operator breaking
rotational invariance. At N=infinity one finds rho=2. 1/N expansion and
strong-coupling calculations show that, for all values of N>=0, rho~2.
  Non-Gaussian corrections to the universal low-momentum behavior of G(x) are
evaluated, and found to be very small.
