Effective Field Approximations for Spin Glass Phase and Random Ordered Phase

The spin glass phase (SGP) and the random ordered phase (ROP) of random quenched Ising spin systems with z ≫1, z being the coordination number, are eximined by the effective field theory. Thereby the effect of the ground-state degeneracies as well as the `frustration effect' are taken into account by a phenomenological parameter. The restricted SGP, which is a SGP but not an ROP, is not found unless obviously incorrect approximation of type \(1{=}{\langle}\sigma^{2}_{i}{\rangle}_{T}{\cong}{\langle}\sigma_{i}{\rangle}^{2}_{T}\) is used, where < > _T indicates the thermal average in a given configuration of the random interactions. We also examine various properties of the ROP, such as the spectrum of the effective field, divergence of the nonlinear susceptibility at the transition point, and the specific heat.