Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-εdimensions
arXiv:cond-mat/9907122 · doi:10.1103/PhysRevB.61.382
Abstract
The large distance behaviors of the random field and random anisotropy O(N) models are studied with the functional renormalization group in 4-εdimensions. 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|^{-0.62ε}. The magnetic susceptibility diverges at low fields as χ\sim H^{-1+0.15ε}. 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.
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