  Equilibrium properties of the three-dimensional isotropic Heisenberg spin
glass are studied by extensive Monte Carlo simulations, with particular
attention to the nature of its phase transition. A finite-size-scaling analysis
is performed both for the spin-glass (SG) and the chiral-glass (CG) orders. Our
results suggest that the model exhibits the CG long-range order at finite
temperatures without accompanying the conventional SG long-range order, in
contrast to some of the recent works claiming the simultaneous SG and CG
transition. Typical length and time scales which represent a crossover from the
spin-chirality coupling regime at short scales to the spin-chirality decoupling
regime at long scales are introduced and examined in order to observe the true
asymptotic transition behavior. On the basis of these crossover scales,
discussion is given concerning the cause of the discrepancy between our present
result and those of other recent numerical works.
