On differentiability of the Parisi formula
Probability
2008-05-04 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.0709.1514,
title = {On differentiability of the Parisi formula},
author = {Dmitry Panchenko},
journal= {arXiv preprint arXiv:0709.1514},
year = {2008}
}