  Spin and chirality orderings of the three-dimensional Heisenberg spin glass
under magnetic fields are studied by large-scale equilibrium Monte Carlo
simulations. It is found that the chiral-glass transition and the chiral-glass
ordered state, which are essentially of the same character as their zero-field
counterparts, occur under magnetic fields. The chiral-glass ordered state
exhibits a one-step-like peculiar replica-symmetry breaking in the chiral
sector, while it does not accompany the spin-glass order perpendicular to the
applied field. Critical perperties of the chiral-glass transition are different
from those of the standard Ising spin glass. Magnetic phase diagram of the
model is constructed, which reveals that the chiral-glass state is quite robust
against magnetic fields. The chiral-glass transition line has a character of
the Gabay-Toulouse line of the mean-field model, yet its physical origin being
entirely different. These numerical results are discussed in light of the
recently developed spin-chirality decoupling-recoupling scenario. Implication
to experimental phase diagram is also discussed.
