Aspelmeier's critical variance conjecture for the SK free energy

Let $F_{N,\beta}$ denote the free energy of the Sherrington–Kirkpatrick model with system size $N$ and inverse temperature $\beta$. At the critical temperature, $\beta=1$.

Aspelmeier's conjecture. The variance satisfies

$${\mathsf{Var}}(F_{N,\beta=1})=\frac16\log N+O(1).$$

This prediction was obtained using non-rigorous physics methods and concerns the fluctuation scale at the phase transition. It has since been confirmed in the paper: the critical variance has logarithmic growth with the stated leading constant.