At critical temperature the SK free energy has variance (1/6) log N + O(1) and a Gaussian CLT, while the annealed overlap satisfies E⟨R_{1,2}²⟩ ≍ N^{-2/3}.
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Fluctuations of the Sherrington-Kirkpatrick free energy at critical temperature
At critical temperature the SK free energy has variance (1/6) log N + O(1) and a Gaussian CLT, while the annealed overlap satisfies E⟨R_{1,2}²⟩ ≍ N^{-2/3}.