For 1 < α < 3/2, the one-dimensional long-range Ising spin glass on the Nishimori line provably has a finite-temperature ferromagnetic phase transition.
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Existence of a Phase Transition in the One-Dimensional Ising Spin Glass Model with Long-Range Interactions on the Nishimori Line
For 1 < α < 3/2, the one-dimensional long-range Ising spin glass on the Nishimori line provably has a finite-temperature ferromagnetic phase transition.