Roughening and preroughening transitions in crystal surfaces with double-height steps

We investigate phase transitions in a solid-on-solid model where double-hei ght steps as well as single-height steps are allowed. Without the double-he ight steps, repulsive interactions between up-up or down-down step pairs gi ve rise to a disordered flat phase. When the double-height steps are allowe d, two single-height steps can merge into a double-height step (step doubli ng). We find that the step doubling reduces repulsive interaction strength between single-height steps and that the disordered flat phase is suppresse d. As a control parameter a step doubling energy is introduced, which is as signed 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 ste p doubling energy.