  We consider a model of a reconstructed crystal surface, first considered by
Villain and Vilfan (Europhys. Lett. 12, p. 523 (1990) and Surf. Sci. 257, p.
368 (1991)) for the gold (110) surface, in which roughening occurs via the
formation of anisotropic steps traversing the entire length of the crystal. The
model is studied by a mapping to a spin--1/2 Fermion system in 1+1 dimensions,
which, in the absence of islands, is precisely the Hubbard model. We consider a
general $\pbyo$ reconstruction, in the presence of inter--step interactions and
closed islands. Our analysis predicts the existence of a new type of rough
phase, with incommensurate correlations in the reconstruction order parameter
and unusual momentum space singularities at a characteristic ``Fermi momentum''
and its harmonics, analagous to the Luttinger liquid of one--dimensional
Fermions. The general phase structure for $p>1$ is as follows: for $p>2$, there
is a flat ordered (FO), a rough incommensurate (RI), and a flat incommensurate
phase (FI). The FO--RI and FO--FI transitions are of the commensurate to
incommensurate type, and the FI--RI transition is in the Kosterlitz--Thouless
(KT) universality class. For $p=2$, the FI phase is replaced by a flat
disordered phase (FD), and there may be a new rough disordered phase (RD). The
FO--FD transition is now of Ising type, and the FD--RD and RI--RD transitions
are in the KT universality class.
