Ordering of the Heisenberg spin glass in high dimensions

Ordering of the Heisenberg spin glass with the nearest-neighbor Gaussian coupling is investigated by equilibrium Monte Carlo simulations in four and five dimensions. Ordering of the mean-field Heisenberg spin glass is also studied for comparison. Particular attention is paid to the nature of the spin-glass and chiral-glass orderings. Our numerical data suggest that, in five dimensions, the model exhibits a single spin-glass transition at a finite temperature, where the spin-glass order accompanying the simultaneous chiral-glass order sets in. In four dimensions, the model exhibits a marginal behavior. Chiral-glass transition at a finite temperature not accompanying the standard spin-glass order is likely to occur, while the critical region associated with the chiral-glass transition is very narrow suggesting that the dimension four is close to the marginal dimensionality.