Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-\epsilon dimensions

TL;DR

This paper investigates the large-distance behavior of random anisotropy and random field O(N) models using functional renormalization group techniques in 4-psilon dimensions, revealing quasi-long-range order and divergence of susceptibility.

Contribution

It introduces a novel approach to study the random field O(N) model without solving complex RG equations, and characterizes the phase with quasi-long-range order in the random anisotropy Heisenberg model.

Findings

The random anisotropy Heisenberg model exhibits a phase with infinite correlation radius at low temperatures.

The magnetization correlation function follows a power law decay with an exponent proportional to psilon.

The magnetic susceptibility diverges as a power law at low fields, with an exponent depending on psilon.

Abstract

The large distance behaviors of the random field and random anisotropy O(N) models are studied with the functional renormalization group in 4-\epsilon dimensions. The random anisotropy Heisenberg (N=3) model is found to have a phase with the infinite correlation radius at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law < m(x) m(y) >\sim |x-y|^{-0.62\epsilon}. The magnetic susceptibility diverges at low fields as \chi \sim H^{-1+0.15\epsilon}. In the random field O(N) model the correlation radius is found to be finite at the arbitrarily weak disorder for any N>3. The random field case is studied with a new simple method, based on a rigorous inequality. This approach allows one to avoid the integration of the functional renormalization group equations.