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 means of Landau--de Gennes theory, displays serious deficiencies, which can only be removed if fluctuations are taken into account within statistical field theory. Here we present details of the calculations. The influence of fluctuations is treated self-consistently within a first order cumulant expansion. The square Δ of the inverse correlation length of the alignment tensor field is introduced as an order parameter. In a simplified model two phases of differing Δ appear at high chiralities, which are identified as the isotropic phase and the isostructural blue fog. The relationship between the cumulant expansion and the Brazovski {} {}{} method is illuminated.