J R L de Almeida and D J Thouless 1978 J. Phys. A: Math. Gen. 11 983 doi:10.1088/0305-4470/11/5/028
J R L de Almeida and D J Thouless
Show affiliationsThe stationary point used by Sherrington and Kirkpatrick (1975) in their evaluation of the free energy of a spin glass by the method of steepest descent is examined carefully. It is found that, although this point is a maximum of the integrand at high temperatures, it is not a maximum in the spin glass phase nor in the ferromagnetic phase at low temperatures. The instability persists in the presence of a magnetic field. Results are given for the limit of stability both for a partly ferromagnetic interaction in the absence of an external field and for a purely random interaction in the presence of a field.
75.10.Nr Spin-glass and other random models
75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.)
82B30 Statistical thermodynamics (See also 80-XX)
82B26 Phase transitions (general)
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
Issue 5 (May 1978)
J R L de Almeida and D J Thouless 1978 J. Phys. A: Math. Gen. 11 983
F Family and T Vicsek 1985 J. Phys. A: Math. Gen. 18 L75