Step-step interactions and correlations from 1D hard-core boson mapping

The theory of the preroughening transition of an unreconstructed surface, and the ensuing disordered hat (DOF) phase, is formulated in terms of steps. Finite terraces play a crucial role in the formulation. We start by mapping the statistical mechanics of interacting (up and down) steps onto the quantum mechanics of two species of one-dimensional hard-core bosons. The finite terraces are generated by a number-non-conserving term in the boson Hamiltonian, which forbids a mapping in terms of fermions.. Once the boson problem is solved, we find the DOF phase is stabilized by short-range repulsions of like steps. On-site repulsion of up-down steps is essential in producing a DOF phase, whereas an off-site attraction between them is favorable but not required. Step-step correlations and terrace width distributions can be directly calculated with this method.