Two-point correlation function of three-dimensional O(N) models: The critical limit and anisotropy

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 rotationally invariant fixed point. Several approaches are exploited, such as strong-coupling expansion of lattice N-vector model, and 1/N expansion, field-theoretical methods within the phi(4) continuum formulation. Non-Gaussian corrections to the universal low-momentum behavior of G (x) are evaluated, and found to be very small. In nonrotationally invariant physical systems with O(N)-invariant interactions, the vanishing of the spatial anisotropy 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. We show that, for all values of N greater than or equal to 0, rho similar or equal to 2.