Monte Carlo simulations of the phase transition of the three-dimensional isotropic Heisenberg spin glass

Equilibrium properties of the three-dimensional isotropic Heisenberg spin glass are studied by extensive Monte Carlo simulations, with particular attention paid to the nature of its phase transition. A finite-size-scaling analysis is performed for both the spin-glass (SG) and 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 a 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.