A Crisanti and C De Dominicis 2010 J. Phys. A: Math. Theor. 43 055002 doi:10.1088/1751-8113/43/5/055002
The Sherrington–Kirkpatrick model near T = Tc: expanding around the replica symmetric solution
A Crisanti1 and C De Dominicis2
Show affiliationsAn expansion for the free energy functional of the Sherrington–Kirkpatrick (SK) model, around the replica symmetric (RS) SK solution Q(RS)ab = δab + q(1 − δab) is investigated. In particular, when the expansion is truncated to the fourth order in Qab − Q(RS)ab the full replica symmetry broken (FRSB) solution is explicitly found but it turns out to exist only in the range of temperature 0.549... ≤ T ≤ Tc = 1, not including T = 0. On the other hand, an expansion around the paramagnetic solution Q(PM)ab = δab, up to the fourth order, yields a FRSB solution that exists in a limited temperature range 0.915... ≤ T ≤ Tc = 1.
- PACS
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75.10.Hk Classical spin models
65.40.G- Other thermodynamical quantities
75.20.-g Diamagnetism, paramagnetism, and superparamagnetism
- MSC
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82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
- Subjects
- Dates
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Issue 5 (5 February 2010)
Received 21 October 2009, in final form 17 December 2009
Published 14 January 2010
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The Sherrington–Kirkpatrick model near T = Tc: expanding around the replica symmetric solution
A Crisanti and C De Dominicis 2010 J. Phys. A: Math. Theor. 43 055002
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