Long-range correlated random field and random anisotropy O(N) models: A functional renormalization group study

Abstract

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.

8 pages, 3 figures, revtex4

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• On Larkin-Imry-Ma State of 3He-A in Aerogel
• Strong orientational effect of stretched aerogel on the 3He order parameter
• Orbital glass and spin glass states of 3He-A in aerogel
• Elastic systems with correlated disorder: Response to tilt and application to surface growth
• Critical behavior of the 2D Ising model with long-range correlated disorder
• A cluster model with random anisotropy for hysteresis jumps in CeNi${}_{1-x}$Cu${}_x$ alloys
• Critical scaling in random-field systems: 2 or 3 independent exponents?
• Critical behavior of the Random-Field Ising Magnet with long range correlated disorder
• Some exact results in branching and annihilating random walks
• Stochastic Inflation and Dimensional Reduction
• Random field and random anisotropy O(N) spin systems with a free surface
• Exact form of the exponential correlation function in the glassy super-rough phase
• Localization of spin waves in disordered quantum rotors
• Stochastic Inflation and Replica Field Theory
• Imry-Ma disordered state induced by defects of "random local anisotropy" type in the system with O(n) symmetry
• Possibility of a continuous phase transition in random-anisotropy magnets with ageneric random-axis distribution
• Cubic anisotropy created by defects of "random local anisotropy" type, and phase diagram of the O(n) model
• Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas
• One-loop functional renormalization group study for the dimensional reduction and its breakdown in the long-range random field O($N$) spin model near lower critical dimension
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Critical Behavior of the Three-Dimensional Random Anisotropy Heisenberg Model
• The Schwartz-Soffer and more inequalities for random fields