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Critical-Window Fluctuations and Disorder Universality for the Sherrington--Kirkpatrick Model
We establish free-energy fluctuation limits for the Ising Sherrington--Kirkpatrick model in the nonzero parts of its critical window. For fixed $b\ne0$ and $β_N=1+bN^{-1/3}\sqrt{\log N}$, our main Gaussian orthogonal ensemble (GOE) result is \[ \sqrt{\frac6{\log N}}\left(F_{N,β_N}-N\,\mathrm{FE}(β
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