On differentiability of the Parisi formula
Dmitry Panchenko, Texas A&M University
Abstract
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 the differentiability to prove non
self-averaging of the overlap outside of the replica symmetric region.
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