The low-temperature Sherrington–Kirkpatrick fluctuation law

For every fixed inverse temperature β > 1, determines the fluctuation scale and limiting law of the zero-field Gaussian Sherrington–Kirkpatrick log partition function. Its variance is asymptotic to $c_\beta n^{1/3}$, with $c_\beta\gt 0$, confirming the predicted n^1/6 standard-deviation scale. Exact centering and standardization give full-sequence convergence to a uniquely characterized nondegenerate law.