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

Campostrini, M. and Pelissetto, A. and Rossi, P. and Vicari, E. (1998) The two-point correlation function of three-dimensional O(N) models: critical limit and anisotropy. Physical review. E, Statistical, nonlinear, and soft matter physics, 57 . p. 184. ISSN 1550-2376

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. Several approaches are exploited, such as strong-coupling expansion of lattice non-linear O(N) sigma models, 1/N-expansion, field-theoretical methods within the phi^4 continuum formulation. In non-rotational invariant physical systems with O(N)-invariant interactions, the vanishing of space-anisotropy approaching the rotational-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=\infty one finds rho=2. We show that, for all values of $N\geq 0$, $\rho\simeq 2$. Non-Gaussian corrections to the universal low-momentum behavior of G(x) are evaluated, and found to be very small.

Repository staff only actions