Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-\epsilon dimensions
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.
Keywords
Cite
@article{arxiv.cond-mat/9907122,
title = {Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-\epsilon dimensions},
author = {D. E. Feldman},
journal= {arXiv preprint arXiv:cond-mat/9907122},
year = {2009}
}
Comments
12 pages, RevTeX; a minor change in the list of references