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Disordered periodic systems at the upper critical dimension

R. Chitra·T. Giamarchi·P. Le Doussal
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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.

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R. Chitra, T. Giamarchi, P. Le Doussal. 1998-09-22. Disordered periodic systems at the upper critical dimension. https://doi.org/10.1103/physrevb.59.4058

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