Pinning and annealing of solitons in modulated systems

Chaotic pinning of solitons occurs in nearly commensurate modulated systems when the distance between solitons becomes so large that their interaction cannot overcome the Peierls pinning potential. We study numerically within the mean-field theory the stability of the randomly pinned ''chaotic'' states as a function of temperature near the commensurate-incommensurate (CI) transition in the axial next-nearest-neighbor Ising model. The pinned state turns into a regular incommensurate state as the temperature is raised. A more regular soliton state emerges as the temperature is lowered. The system never reaches the ground state (Frank and van der Merwe or devil's-staircase behavior) near the CI transition because of the pinning. The chaos and the hysteresis may explain recent experimental findings in magnetic and ferroelectric systems