English

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

Disordered Systems and Neural Networks 2009-10-31 v3 Statistical Mechanics

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