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The ordering of the one-dimensional Heisenberg spin glass interacting via thelong-range power-law interaction is studied by Monte Carlo simulations.Particular attention is paid to the possible occurrence of the ``spin-chiralitydecoupling'' for appropriate values of the power-law exponent \sigma. Ourresult suggests that, for intermediate values of $\sigma$, the chiral-glassorder occurs at finite temperatures while the standard spin-glass order occursonly at zero temperature.Comment: Proceedings of the Highly Frustrated Magnetism (HFM2006) conference.  To appear in a special issue of J. Phys. Condens. Matte

Spin and chirality orderings of the one-dimensional Heisenberg spin glass with long-range power-law interaction