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}.
and Kang, Taegu , title=
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Proves O(log N) upper bound and Omega(log log log N) lower bound on Var(F_N(1)) at criticality in the SK model.
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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}.
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The Order of Free Energy Fluctuations in the Critical Sherrington-Kirkpatrick Model Revisited
Proves O(log N) upper bound and Omega(log log log N) lower bound on Var(F_N(1)) at criticality in the SK model.