2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160148It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using approximate solutions in the Parisi formula and give one example of application of the differentiability to prove non self-averaging of the overlap outside of the replica symmetric region.ProbabilityMathematical Physics60K35, 82B44text