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Abstract
Conventional mean-field theory renders the structure of the cubic blue phases correctly, but not their position on the phase diagram. Also it has not been possible to suppress the artificial body centered cubic structure O5. Within the framework of the weak crystallization theory we extend the Landau-Ginzburg-de Gennes free energy by including order parameter fluctuations. Calculations that involve one star of wave vectors destabilize the formerly dominant O5 structure.