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In this review we consider glass states of several disordered systems:vortices in impure superconductors, amorphous magnets, and nematic liquidcrystals in random porous media. All these systems can be described by therandom-field or random-anisotropy O(N) model. Even arbitrarily weak disorderdestroys long range order in the O(N) model. We demonstrate that at weakdisorder and low temperatures quasi-long range order emerges. Inquasi-long-range-ordered phases the correlation length is infinite andcorrelation functions obey power dependencies on the distance. In pure systemsquasi-long range order is possible only in the lower critical dimension andonly in the case of Abelian symmetry. In the presence of disorder this type ofordering turns out to be more common. It exists in a range of dimensions and isnot prohibited by non-Abelian symmetries.Comment: 32 page

QUASI-LONG RANGE ORDER IN GLASS STATES OF IMPURE LIQUID CRYSTALS, MAGNETS, AND SUPERCONDUCTORS