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

TL;DR

This paper studies the critical behavior and anisotropy in the two-point correlation function of three-dimensional O(N) models, revealing universal properties and small non-Gaussian corrections near the rotationally-invariant fixed point.

Contribution

It introduces a detailed analysis of anisotropy vanishing characterized by a universal critical exponent and evaluates non-Gaussian corrections across different N values.

Findings

Critical exponent rho is approximately 2 for all N>=0.

Anisotropy vanishes with a universal exponent rho.

Non-Gaussian corrections to G(x) are very small.

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 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.