Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 13 (2008), paper no. 23, 241-247.
On differentiability of the Parisi formula
It was proved by Michel Talagrand in  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.
Electron. Commun. Probab., Volume 13 (2008), paper no. 23, 241-247.
Accepted: 4 May 2008
First available in Project Euclid: 6 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
This work is licensed under aCreative Commons Attribution 3.0 License.
Panchenko, Dmitry. On differentiability of the Parisi formula. Electron. Commun. Probab. 13 (2008), paper no. 23, 241--247. doi:10.1214/ECP.v13-1365. https://projecteuclid.org/euclid.ecp/1465233450