Critical limit and anisotropy in the two-point correlation function of three-dimensional O(N) models

Dipartimento di Fisica dell'Università and INFN - I-56126 Pisa, Italy

Received: 9 April 1997
Accepted: 13 May 1997

Abstract

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 rotational-invariant fixed point. In non-rotational invariant physical systems with -invariant interactions, the vanishing of space-anisotropy approaching the rotational-invariant fixed point is described by a critical exponent ρ, which is universal and is related to the leading irrelevant operator breaking rotational invariance. At one finds . We show that, for all values of , . Non-Gaussian corrections to the universal low-momentum behavior of G(x) are evaluated, and found to be very small.