The low-temperature Sherrington–Kirkpatrick free-energy limiting law

For every fixed inverse temperature β > 1, we prove that the zero-field Gaussian Ising Sherrington–Kirkpatrick free energy, centered by its expectation and divided by its standard deviation, converges in distribution to a nondegenerate law as the system size tends to infinity through all integers. We also prove that its variance divided by n${}^{1/3}$ converges to a finite positive constant.