  We discuss the results of a study of restricted solid-on-solid models for fcc
(110) surfaces. These models are simple modifications of the exactly solvable
BCSOS model, and are able to describe a $(2\times 1)$ missing-row reconstructed
surface as well as an unreconstructed surface. They are studied in two
different ways. The first is by mapping the problem onto a quantum spin-1/2
one-dimensional hamiltonian of the Heisenberg type, with competing $S^z_iS^z_j$
couplings. The second is by standard Monte Carlo simulations. We find phase
diagrams with the following features, which we believe to be quite generic: (i)
two flat, ordered phases (unreconstructed and missing-row reconstructed); a
rough, disordered phase; an intermediate disordered flat (DF) phase,
characterized by monoatomic steps, whose physics is shown to be akin to that of
a dimer spin state. (ii) a transition line from the $(2\times 1)$ reconstructed
phase to the DF phase showing exponents which appear to be close, within our
numerical accuracy, to the 2D-Ising universality class. (iii) a critical
(preroughening) line with variable exponents, separating the unreconstructed
phase from the DF phase. Possible signatures and order parameters of the DF
phase are investigated.
