On Differentiability of the Parisi Formula
نویسندگان
چکیده
It 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 differentiability to prove non self-averaging of the overlap outside of the replica symmetric region.
منابع مشابه
ar X iv : 0 70 9 . 15 14 v 1 [ m at h . PR ] 1 1 Se p 20 07 On differentiability of the Parisi formula .
It was proved in [7] that Parisi formula is differentiable with respect to inverse temperature parameter. We obtain a simpler proof of this result by using approximate solutions in the Parisi formula and give one example of application to replica symmetry breaking.
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