Electronic Communications in Probability

On differentiability of the Parisi formula

Dmitry Panchenko

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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

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

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

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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.)

Sherrington-Kirkpatrick model Parisi formula

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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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