2-loop Functional Renormalization for elastic manifolds pinned by disorder in N dimensions

Abstract

We study elastic manifolds in a N-dimensional random potential using functional RG. We extend to N>1 our previous construction of a field theory renormalizable to two loops. For isotropic disorder with O(N) symmetry we obtain the fixed point and roughness exponent to next order in epsilon=4-d, where d is the internal dimension of the manifold. Extrapolation to the directed polymer limit d=1 allows some handle on the strong coupling phase of the equivalent N-dimensional KPZ growth equation, and eventually suggests an upper critical dimension of about 2.5.

4 pages, 3 figures

References in corpus (3)

• Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
• Derivation of the Functional Renormalization Group Beta-Function at order 1/N for Manifolds Pinned by Disorder
• X-ray spectrum of a pinned charge density wave

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• Stability of Random-Field and Random-Anisotropy Fixed Points at large N
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• Upper critical dimension of the KPZ equation
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• Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer formulation
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• Freezing transition of the directed polymer in a $1+d$ random medium : location of the critical temperature and unusual critical properties
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• Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
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• Disorder-dominated phases of random systems : relations between tails exponents and scaling exponents
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• Field Theory of Disordered Elastic Interfaces at 3-Loop Order: The $\beta$-Function
• Patterns in the Kardar-Parisi-Zhang equation
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• Uniform fluctuation and wandering bounds in first passage percolation
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