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(4+N)-Dimensional Elastic Manifolds in Random Media: a Renormalization-Group Analysis | | H. Bucheli
; O.S. Wagner
; V.B. Geshkenbein
; A.I. Larkin
; G. Blatter
; | | Date: |
6 Dec 1997 | | Subject: | Superconductivity; Disordered Systems and Neural Networks | cond-mat.supr-con cond-mat.dis-nn | | Abstract: | Motivated by the problem of weak collective pinning of vortex lattices in high-temperature superconductors, we study the model system of a four-dimensional elastic manifold with N transverse degrees of freedom (4+N-model) in a quenched disorder environment. We assume the disorder to be weak and short-range correlated, and neglect thermal effects. Using a real-space functional renormalization group (FRG) approach, we derive a RG equation for the pinning-energy correlator up to two-loop correction. The solution of this equation allows us to calculate the size R_c of collectively pinned elastic domains as well as the critical force F_c, i.e., the smallest external force needed to drive these domains. We find R_c prop. to delta_p^alpha_2 exp(alpha_1/delta_p) and F_c prop. to delta_p^(-2 alpha_2) exp(-2 alpha_1/delta_p), where delta_p <<1 parametrizes the disorder strength, alpha_1=(2/pi)^(N/2) 8 pi^2/(N+8), and alpha_2=2(5N+22)/(N+8)^2. In contrast to lowest-order perturbation calculations which we briefly review, we thus arrive at determining both alpha_1 (one-loop) and alpha_2 (two-loop). | | Source: | arXiv, cond-mat/9801036 | | Services: | Forum | Review | PDF | Favorites | |
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