Nonergodic behavior in the Ising model with transverse field

The mode coupling approximation is used to study the nonergodic behavior of the Ising model with transverse field in terms of the time correlation functions of the longitudinal and transverse spin components. It is shown that there exists a lower critical value of the transverse field, $\Omega=\Omega_c^0$, such that when $\Omega<\Omega_c^0$ the system is nonergodic at all temperatures, like the ordinary Ising model. For $\Omega_c^0<\Omega<\Omega_c$ ($\Omega_c$ is the upper critical value, at which the phase transition in the model disappears) nonergodic behavior appears at a temperature $T_f>T_c$, where $T_c$ is the temperature of the phase transition. The interval of nonergodicity contracts, $T_f-T_c\to 0$, as $\Omega\to\Omega_c$, and $T_f-T_c\to\infty$ as $\Omega\to\Omega_c^0$.