English

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}
}
R2 v1 2026-06-21T09:16:01.308Z