Stability of the Sherrington-Kirkpatrick solution of a spin glass model

作者：J. R. L. de Almeida, D. J. Thouless · 发表于：Journal of Physics A Mathematical and General · 年份：1978 · DOI：10.1088/0305-4470/11/5/028 · 被引用次数：2067 · 研究领域：Theoretical and Computational Physics、Complex Systems and Time Series Analysis、Material Dynamics and Properties

The 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.