Quantum transverse Ising spin-glass model in the mean-field approximation

A mean-field approximation is used to investigate the quantum transverse Ising spin-glass model in the Edwards-Anderson version. We introduce two order parameters, diagonal and off diagonal in replica indices, and discuss their physical significance. The effective free-energy function is obtained, and the critical value of the transverse field $\Gamma$ at zero temperature is calculated. We find the behavior of the order parameters near the zero-temperature critical point. The phase diagram in the $\Gamma$,$T$ plane is also given.