3D long range order

Mayoral, R. et al., 3D long-range ordering in an SiOj submicrometer-sphere sintered superstructure, Adv. Mater, 9, 257, 1997. 

For systems which are strictly two-dimensional, of course, only an Ising model (which we believe to be appropriate for the present materials) will exhibit true long-range order at finite temperature. However, even for the cases of xy or Heisenberg spins, 3D long-range order will be induced for < Jab- In the conventional two-dimensional systems... 

The electrical conductivity of GdBigSig follows the 3D variable range hopping (VRH) dependence that is typical of the icosahedral higher borides, and it exhibits a 3D long-range-order antiferromagnetic transition at Tn = 3.2... 

Many methods to control 3D block copolymer nanostructures have been reviewed here, with particular attention paid to achieving long-range order... 

Soft X-ray spectroscopy has been used to investigate the 3d electron distribution in small Ni particles.179 180 In addition to showing modified absorption and emission spectra, the small Ni particles (< 2 nm) have two satellite peaks in the absorption spectrum missing. This is attributed to a loss of long range order due to small particle size. 

If a liquid is reversibly cooled below the melting point, the solid, i.e., a three-dimensional giant molecule ( 3D polymer ) forms, characterized by a long range order. So-formed crystals exhibit strict periodicity. While, in the case of liquids, structural configurations fluctuate in space and time, glasses as frozen liquids or other amorphous solids show also fluctuations but essentially only with respect to the position coordinate. 

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