Quasi-long-range order in the random anisotropy Heisenberg model: Functional renormalization group in 4-ɛ 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-ɛ 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(r1)m(r2)>~\|r1-r2\|-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 renormalization-group equations.
- Publication:
-
Physical Review B
- Pub Date:
- January 2000
- DOI:
- 10.1103/PhysRevB.61.382
- arXiv:
- arXiv:cond-mat/9907122
- Bibcode:
- 2000PhRvB..61..382F
- Keywords:
-
- 75.10.Nr;
- 64.60.Cn;
- 75.50.Kj;
- Spin-glass and other random models;
- Order-disorder transformations;
- statistical mechanics of model systems;
- Amorphous and quasicrystalline magnetic materials;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 12 pages, RevTeX