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Spin and chirality orderings of the three-dimensional Heisenberg spin glassunder magnetic fields are studied by large-scale equilibrium Monte Carlosimulations. It is found that the chiral-glass transition and the chiral-glassordered state, which are essentially of the same character as their zero-fieldcounterparts, occur under magnetic fields. The chiral-glass ordered stateexhibits a one-step-like peculiar replica-symmetry breaking in the chiralsector, while it does not accompany the spin-glass order perpendicular to theapplied field. Critical perperties of the chiral-glass transition are differentfrom those of the standard Ising spin glass. Magnetic phase diagram of themodel is constructed, which reveals that the chiral-glass state is quite robustagainst magnetic fields. The chiral-glass transition line has a character ofthe Gabay-Toulouse line of the mean-field model, yet its physical origin beingentirely different. These numerical results are discussed in light of therecently developed spin-chirality decoupling-recoupling scenario. Implicationto experimental phase diagram is also discussed.Comment: 23 pages, 23 figure

Monte Carlo Studies of the Ordering of the Three-Dimensional Isotropic Heisenberg Spin Glass in Magnetic Fields