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 $\ensuremath{\Gamma}$ at zero temperature is calculated. We find the behavior of the order parameters near the zero-temperature critical point. The phase diagram in the $\ensuremath{\Gamma}$,
T plane is also given.
We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to
L=40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain
Tc=1.1019(29) for the critical temperature, $\ensuremath{\nu}=2.562(42)$ for the thermal exponent, $\ensuremath{\eta}=\ensuremath{-}0.3900(36)$ for the anomalous dimension, and $\ensuremath{\omega}=1.12(10)$ for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield $\ensuremath{\alpha}=\ensuremath{-}5.69(13)$, $\ensuremath{\beta}=0.782(10)$, and $\ensuremath{\gamma}=6.13(11)$. We also compute several universal quantities at
Tc.