Disordered periodic systems at the upper critical dimension
Disordered Systems and Neural Networks
2009-10-31 v1
Abstract
The effects of weak point-like disorder on periodic systems at their upper critical dimension D_c for disorder are studied. The systems studied range from simple elastic systems with D_c=4 to systems with long range interactions with D_c=2 and systems with D_c=3 such as the vortex lattice with dispersive elastic constants. These problems are studied using the Gaussian Variational method and the Functional Renormalisation Group. In all the cases studied we find a typical ultra-slow loglog(x) growth of the asymptotic displacement correlation function, resulting in nearly perfect translational order. Consequences for the Bragg glass phase of vortex lattices are discussed.
Cite
@article{arxiv.cond-mat/9809300,
title = {Disordered periodic systems at the upper critical dimension},
author = {R. Chitra and T. Giamarchi and P. Le Doussal},
journal= {arXiv preprint arXiv:cond-mat/9809300},
year = {2009}
}
Comments
12 RevTex pages, uses epsfig, 2 figures