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The Sherrington–Kirkpatrick model near T = Tc: expanding around the replica symmetric solution

A Crisanti1 and C De Dominicis2

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An 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 QabQ(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... ≤ TTc = 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... ≤ TTc = 1.


PACS

75.10.Hk Classical spin models

65.40.G- Other thermodynamical quantities

75.20.-g Diamagnetism, paramagnetism, and superparamagnetism

MSC

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

82D40 Magnetic materials

82B30 Statistical thermodynamics (See also 80-XX)

Subjects

Condensed matter: electrical, magnetic and optical

Condensed matter: structural, mechanical & thermal

Dates

Issue 5 (5 February 2010)

Received 21 October 2009, in final form 17 December 2009

Published 14 January 2010



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