Physics – Condensed Matter
Scientific paper
2003-04-27
Phys.Rev.E69:026112,2004
Physics
Condensed Matter
42 pages, 41 figures
Scientific paper
10.1103/PhysRevE.69.026112
We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the renormalization group functions beyond 1-loop order. Even worse, observables such as the 2-point correlation function exhibit the same problem already at 1-loop order. These difficulties are due to the non-analyticity of the renormalized disorder correlator at zero temperature, which is inherent to the physics beyond the Larkin length, characterized by many metastable states. As a result, 2-loop diagrams, which involve derivatives of the disorder correlator at the non-analytic point, are naively "ambiguous''. We examine several routes out of this dilemma, which lead to a unique renormalizable field-theory at 2-loop order. It is also the only theory consistent with the potentiality of the problem. The beta-function differs from previous work and the one at depinning by novel "anomalous terms''. For interfaces and random bond disorder we find a roughness exponent zeta = 0.20829804 epsilon + 0.006858 epsilon^2, epsilon = 4-d. For random field disorder we find zeta = epsilon/3 and compute universal amplitudes to order epsilon^2. For periodic systems we evaluate the universal amplitude of the 2-point function. We also clarify the dependence of universal amplitudes on the boundary conditions at large scale. All predictions are in good agreement with numerical and exact results, and an improvement over one loop. Finally we calculate higher correlation functions, which turn out to be equivalent to those at depinning to leading order in epsilon.
Chauve Pascal
Doussal Pierre Le
Wiese Kay Joerg
No associations
LandOfFree
Functional Renormalization Group and the Field Theory of Disordered Elastic Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Functional Renormalization Group and the Field Theory of Disordered Elastic Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Functional Renormalization Group and the Field Theory of Disordered Elastic Systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-44794