A Dynamical Theory of Random Quenched System and Its Application to Infinite-Ranged Ising Model

A dynamical thoery for quenched random systems is developed in the framework of the closed time–path Green's functions (CTPGF). The order parameter q, a matrix in general, appears naturally as an integral part of the second order connected CTPGF. An equation to determine q is derived from the Dyson-Schwinger equation. The formalism developed is applied to the study of the long-ranged random Ising model. A boundary line is found on the q-|χ| plane. It is argued that the spin–glass phase is characterized by the fixed point lying on the stability boundary. The magnetization is calculated in perturbation and is found to be in good agreement with those predicted by the projection hypothesis. The general validity of the projection hypothesis is discussed.