The Two-point Correlation Function of Three-dimensional O(n ) Models: Critical Limit and Anisotropy. Typeset Using Revt E X 1

In three-dimensional O(N) models, we investigate the low-momentum be-havior of the two-point Green’s function G(x) in the critical region of thesymmetric phase. We consider physical systems whose criticality is charac-terized by a rotational-invariant fixed point. Several approaches are exploited,such as strong-coupling expansion of lattice non-linear O(N) σ models, 1/N -expansion, field-theoretical methods within the φ4 continuum formulation.Non-Gaussian corrections to the universal low-momentum behavior ofG(x) are evaluated, and found to be very small.In non-rotational invariant physical systems with O(N)-invariant interac-tions, the vanishing of space-anisotropy approaching the rotational-invariantfixed point is described by a critical exponent ρ, which is universal and isrelated to the leading irrelevant operator breaking rotational invariance. AtN = ∞ one finds ρ = 2. We show that, for all values of N ≥ 0, ρ ≃ 2. PACS numbers: 05.70.Jk, 64.60.Fr, 75.10.Hk, 75.40.Cx Typeset using REVTEX