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Preroughening transitions take place in equilibrium crystal surfaces,
typically near surface roughening transitions.

DOF phases are mathematically equivalant to socalled valence bond phases in one dimensional quantum spin chains (via the socalled transfer matrix formalism). The latter are quantum liquids with topological long range order with soliton like excitations. This equivalence elucidated the nature of long range order in the latter. 
In our early work, stepstep interactions where required to stabilize DOF phases, but later we realized that directional anisotropy in step energies and more complex crystaline unit cells can have the same effect, e.g., in Si(001) and in Naphtalene. 