Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2002-01-15
Int. J. Mod. Phys. B 15, 2945 (2001)
Physics
Condensed Matter
Disordered Systems and Neural Networks
32 pages
Scientific paper
10.1142/S0217979201006641
In this review we consider glass states of several disordered systems: vortices in impure superconductors, amorphous magnets, and nematic liquid crystals in random porous media. All these systems can be described by the random-field or random-anisotropy O(N) model. Even arbitrarily weak disorder destroys long range order in the O(N) model. We demonstrate that at weak disorder and low temperatures quasi-long range order emerges. In quasi-long-range-ordered phases the correlation length is infinite and correlation functions obey power dependencies on the distance. In pure systems quasi-long range order is possible only in the lower critical dimension and only in the case of Abelian symmetry. In the presence of disorder this type of ordering turns out to be more common. It exists in a range of dimensions and is not prohibited by non-Abelian symmetries.
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