Phase transitions in the one-dimensional long-range diluted Heisenberg spin glass

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.