Quasilongrange order in the random anisotropy Heisenberg model: Functional renormalization group in 4ɛ dimensions
Abstract
The largedistance behaviors of the random field and random anisotropy O(N) models are studied with the functional renormalization group in 4ɛ dimensions. The random anisotropy Heisenberg (N=3) model is found to have a phase with an infinite correlation length at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law <m(r_{1})m(r_{2})>~\r_{1}r_{2}\^{0.62ɛ}. The magnetic susceptibility diverges at low fields as χ~H^{1+0.15ɛ}. In the random field O(N) model the correlation length is found to be finite at the arbitrarily weak disorder for any N>3. The random field case is studied with a simple method, based on a rigorous inequality. This approach allows one to avoid the integration of the functional renormalizationgroup equations.
 Publication:

Physical Review B
 Pub Date:
 January 2000
 DOI:
 10.1103/PhysRevB.61.382
 arXiv:
 arXiv:condmat/9907122
 Bibcode:
 2000PhRvB..61..382F
 Keywords:

 75.10.Nr;
 64.60.Cn;
 75.50.Kj;
 Spinglass and other random models;
 Orderdisorder transformations;
 statistical mechanics of model systems;
 Amorphous and quasicrystalline magnetic materials;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 12 pages, RevTeX