Directed Ising type dynamic preroughening transition in one dimensional interfaces

We present a realization of directed Ising (DI) type dynamic absorbing state phase transitions in the context of one-dimensional interfaces, such as the relaxation of a step on a vicinal surface. Under the restriction that particle deposition and evaporation can only take place near existing kinks, the interface relaxes into one of three steady states: rough, perfectly ordered flat (OF) without kinks, or disordered flat (DOF) with randomly placed kinks but in perfect up-down alternating order. A DI type dynamic preroughening transition takes place between the OF and DOF phases. At this critical point the asymptotic time evolution is controlled not only by the DI exponents but also by the initial condition. Information about the correlations in the initial state persists and changes the critical exponents.