The phase diagram of the Ising spin glass model in a transverse field is studied by the local mean field method. Effects of the transverse field on specific heat, irreversibility and hysteresis are elucidated.
The classical transverse field Ising spin-glass model with short-range interactions is investigated beyond the mean-field approximation for a real d -dimensional lattice. We use an appropriate non-trivial modification of the Bethe-Peierls method recently formulated for the Ising spin-glass. The zero-temperature critical value of the transverse field and the linear susceptibility in the paramagnetic phase are obtained analytically as functions of dimensionality d . The phase diagram is also calculated numerically for different values of d . In the limit , known mean-field results are consistently reproduced.
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 study the three-dimensional quantum Ising spin glass in a transverse magnetic field following the evolution of the bond probability distribution under renormalization-group transformations. The phase diagram (critical temperature Tc vs transverse field \ensuremath{\Gamma}) we obtain shows a finite slope near T=0, in contrast with the infinite slope for the pure case. Our results compare very well with the experimental data recently obtained for the dipolar Ising spin glass LiHo0.167Y0.833F4, in a transverse field. This indicates that this system is more appropriately described by a model with short-range interactions than by an equivalent Sherrington-Kirkpatrick model in a transverse field.