Disordered Flat Phase in a Solid on Solid Model of Fcc(110) Surfaces and   Dimer States in Quantum Spin-1/2 Chains
  We present a restricted solid on solid hamiltonian for fcc (110) surfaces. It is the simplest generalization of the exactly solvable BCSOS model which is able to describe a $(2\times 1)$ missing-row reconstructed surface. We study this model by mapping it onto a quantum spin-1/2 chain of the Heisenberg type, with second and third neighbor $S^z_iS^z_j$ couplings. The ground state phase diagram of the spin-chain model is studied by exact diagonalization of finite chains up to $N=28$ sites, as well as through analytical techniques. We find four phases in the phase diagram: two ordered phases in which the spins have a N\'eel-type of long range order (an unreconstructed and a missing-row reconstructed phase, in the surface language), a spin liquid phase (representing a rough surface), and an intermediate dimer phase which breaks translational invariance and has a doubly degenerate ground state, corresponding to a disordered flat surface. The transition from the $(2\times 1)$ reconstructed phase to the disordered flat phase belongs to the $2D$ Ising universality class. A critical (preroughening) line with varying exponents separates the unreconstructed phase from the disordered flat phase. The possible experimental signatures of the disordered flat phase are discussed. 
Giuseppe Santoro and Michele Fabrizio