  We use Monte Carlo simulations to study the one-dimensional long-range
diluted Heisenberg spin glass with interactions that fall as a power, sigma, of
the distance. Varying the power is argued to be equivalent to varying the space
dimension of a short-range model. We are therefore able to study both the
mean-field and non-mean-field regimes. For one value of sigma, in the
non-mean-field regime, we find evidence that the chiral glass transition
temperature may be somewhat higher than the spin glass transition temperature.
For the other values of sigma we see no evidence for this.
