We study the dynamical magnetization process in the ordered ground-state phase of the transverse Ising model under sweeps of magnetic field with constant velocities. In the case of very slow sweeps and for small systems studied previously [H. De Raedt et al., Phys. Rev. B 56, 11761 (1997)], nonadiabatic transitions at avoided level-crossing points give the dominant contribution to the shape of magnetization process. In contrast, in the ordered phase of this model and for fast sweeps, we find significant size-independent jumps in the magnetization process. We study this phenomenon in analogy to the spinodal decomposition in classical ordered state and investigate its properties and its dependence on the system parameters. An attempt to understand the magnetization dynamics under field sweep in terms of the energy-level structure is made. We discuss a microscopic mechanism of magnetization dynamics from a viewpoint of local cluster flips and show that this provides a picture that explains the size independence. The magnetization dynamics in the fast-sweep regime is studied by perturbation theory and we present a perturbation scheme based on interacting Landau-Zener-type processes to describe the local cluster flip dynamics.

• Received 27 November 2008

DOI:https://doi.org/10.1103/PhysRevB.79.104422