Phase diagrams of the liquid-crystalline blue phases (BPs), as calcula
ted by means of Landau theory, display two serious deficiencies: They
contain a never-observed structure of space group O-5, and BP II does
not disappear at very high chiralities. Here we prove by a first-order
cumulant expansion that neglect of fluctuations is the cause. We also
observe a smooth transition from a strongly to a weakly correlated is
otropic phase, which vanishes at large chiralities. It indicates the e
xistence of a critical point and characterizes BP III as a second isot
ropic phase, in agreement with recent experiments.