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We discuss the results of a study of restricted solid-on-solid model Hamiltonians for fee (110) surfaces. These models are simple modifications of the exactly solvable body-centered solid-on-solid model, and are able to describe a (2x1) 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 (SiSjz)-S-z couplings. The second is by standard two-dimensional 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 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 (2x1) reconstructed phase to the disordered flat phase showing exponents that appear to be close, within our numerical accuracy, to the two-dimensional Ising universality class. (iii) A critical (preroughening) line with variable exponents, separating the unreconstructed phase from the disordered flat phase. Possible signatures and order parameters of the disordered flat phase are investigated

Disordered flat phase and phase diagram for restricted solid-on-solid models of fcc (110) surfaces