Abstract
The preroughening transition of a surface and the ensuing disordered flat (DOF) phase are discussed in terms of steps, by taking into account their interactions as well as the crucial role of finite terraces. 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 effect of finite terraces translates into a number-non-conserving term in the boson Hamiltonian, which does not allow a description in terms of fermions, but leads to a two-chain spin problem. The global phase diagram is rich. The DOF phase is found, once again, to be the translation of the well-known Haldane-gapped phase of a spin-1 Heisenberg antiferromagnet. The preroughening transition from the flat to the DOF phase, as a function of the step chemical potential, is also discussed.
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