Influence of fluctuations on the phase diagram of chiral nematic liquid crystals

In a recent paper [Phys. Rev. Lett. 81, 1457 (1998)], we demonstrated that the phase diagram of the liquid crystalline blue phases, as calculated by m eans of Landau-de Gennes theory, displays serious deficiencies, which can o nly be removed if fluctuations are taken into account within statistical fi eld theory. Here we present details of the calculations. The influence of f luctuations is treated self-consistently within a first order cumulant expa nsion. The square Delta of the inverse correlation length of the alignment tensor field is introduced as an order parameter. In a simplified model two phases of differing Delta. appear at high chiralities, which are identifie d as the isotropic phase and the isostructural blue fog. The relationship b etween the cumulant expansion and the Brazovskii method is illuminated.