Phase Transition of the Sherrington-Kirkpatrick Model

抄録

The free energy of the Sherrington-Kirkpatrick (SK) model for the spin glass is calculated exactly as a function of local magnetic moments in the form of power expansion. The expression is shown to coincide with that of Thouless, Anderson and Palmer and with that of Oguchi and Takano up to the fourth order term, suggesting that the Bethe or the pair approximation is exact for this model. The transition temperature obtained from the second order term gives the SK transition line. It is shown that the linear susceptibility diverges at the ferromagnetic transition temperature and remains finite at the spin glass one, and that the nonlinear susceptibility diverges negatively both at the spin glass and the ferromagnetic transition temperatures. The nature of the phase transition is seen to be rather peculiar and the more detailed analysis of higher order terms is necessary to obtain the definite conclusion.