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The one-dimensional long-range Ising spin glass provides useful insights intothe properties of finite dimensional spin glasses with short-rangeinteractions. The defect energy renormalization group equations derived for itby Kotliar, Anderson and Stein have been re-examined and a new fixed point hasbeen found. The fixed points which have previously been studied are found to beinappropriate. It is shown that the renormalization group equations themselvesdirectly imply that the spin glass phase is replica symmetric, in agreementwith droplet model expectations, when the range exponent $\sigma$ lies betweenthe upper and lower critical values.

The ordered phase of the one-dimensional Ising spin glass with long-range interactions