Preroughening transitions in a model for Si(001)- and Ge(001)-type crystal surfaces

The uniaxial structure of Si(001) and Ge(001) facets leads to nontrivial topological properties of steps and hence to interesting equilibrium phase transitions. The disordered flat phase and the preroughening transition can be stabilized without the need for step-step interactions. A model describing this is studied numerically by transfer matrix-type finite-size-scaling of interface free energies. Its phase diagram contains a flat, rough, and disordered flat phase, separated by roughening and preroughening transition lines. Our estimate for the location of the multicritical point where the preroughening line merges with the roughening line, predicts that Si(001) and Ge(001) undergo preroughening-induced simultaneous deconstruction transitions.