Roughening and preroughening transitions in crystal surfaces with   double-height steps
  We investigate phase transitions in a solid-on-solid model where double-height steps as well as single-height steps are allowed. Without the double-height steps, repulsive interactions between up-up or down-down step pairs give rise to a disordered flat phase. When the double-height steps are allowed, two single-height steps can merge into a double-height step (step doubling). We find that the step doubling reduces repulsive interaction strength between single-height steps and that the disordered flat phase is suppressed. As a control parameter a step doubling energy is introduced, which is assigned to each step doubling vertex. From transfer matrix type finite-size-scaling studies of interface free energies, we obtain the phase diagram in the parameter space of the step energy, the interaction energy, and the step doubling energy. 
Jae Dong Noh