Ordering in the quenched two-dimensional axial next-nearest-neighbor Ising model

Monte Carlo simulations of ordering in the two-dimensional axial next-nearest-neighbor Ising model following a quench were performed using nonconserved dynamics for a wide range of frustration parameters, κ, and temperatures. It was found that in quenches from T≫T_c to T<T_c for κ≤0 (i.e., in the ferromagnetic regime) ordered domains form quickly and coarsen with the expected t^1/2 kinetics. Similar results are found for quenches at κ≥1, where the ordered structure is striped. However, for 0<κ<1, quenches to low temperature produce a disordered, glassy phase, which shows logrithmic ordering kinetics and is insensitive to whether the underlying ground state is ferromagnetic or 2 phase (i.e., striped phase). Quenches to higher temperatures show the presence of a finite glass-transition temperature. Discontinuous changes in the value of the frustration parameter from the ferromagnetic to the 2-phase region of the phase diagram at low temperature yields a phase change which occurs via classical nucleation and growth. A simple energetic or growth model is proposed which accounts for all of the temperatures at which the ordering kinetics undergoes transitions.