Electronic Communications in Probability

On differentiability of the Parisi formula

Dmitry Panchenko

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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.

Article information

Source
Electron. Commun. Probab., Volume 13 (2008), paper no. 23, 241-247.

Dates
Accepted: 4 May 2008
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465233450

Digital Object Identifier
doi:10.1214/ECP.v13-1365

Mathematical Reviews number (MathSciNet)
MR2399285

Zentralblatt MATH identifier
1205.82092

Subjects
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.)

Keywords
Sherrington-Kirkpatrick model Parisi formula

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


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References

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