  We present extensive numerical studies to determine the phase diagrams of
cubic and hexagonal blue phases in an electric field. We confirm the earlier
prediction that hexagonal phases, both 2 and 3 dimensional, are stabilized by a
field, but we significantly refine the phase boundaries, which were previously
estimated by means of a semi-analytical approximation. In particular, our
simulations show that the blue phase I -- blue phase II transition at fixed
chirality is largely unaffected by electric field, as observed experimentally.
