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Critical Free-Energy Variance in the Sherrington-Kirkpatrick Model
We study the normalized free energy $F_N=N^{-1}\log Z_N$ of the Sherrington-Kirkpatrick model at the critical point $(β,h)=(1,0)$, and prove the unconditional variance bound \[ \mathrm{Var}\,F_N(1)\le\frac{1}{2N^2}\logχ_{\mathrm{SG}}(N)+O(N^{-2}), \] where $χ_{\mathrm{SG}}(N)$ is the finite-size spi
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