Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2007-01-11
Phys. Rev. B 75, 174206 (2007)
Physics
Condensed Matter
Disordered Systems and Neural Networks
8 pages, 3 figures, revtex4
Scientific paper
10.1103/PhysRevB.75.174206
We study the long-distance behavior of the O(N) model in the presence of random fields and random anisotropies correlated as ~1/x^{d-sigma} for large separation x using the functional renormalization group. We compute the fixed points and analyze their regions of stability within a double epsilon=d-4 and sigma expansion. We find that the long-range disorder correlator remains analytic but generates short-range disorder whose correlator develops the usual cusp. This allows us to obtain the phase diagrams in (d,sigma,N) parameter space and compute the critical exponents to first order in epsilon and sigma. We show that the standard renormalization group methods with a finite number of couplings used in previous studies of systems with long-range correlated random fields fail to capture all critical properties. We argue that our results may be relevant to the behavior of He-3A in aerogel.
Fedorenko Andrei A.
Kuhnel Florian
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