  We introduce a {\it lattice} version of the Calogero Sutherland model adapted
to describe $1/d^2$ pairwise interacting steps with discrete positions on a
vicinal surface. The configurational free energy is obtained within a transfer
matrix method. The full phase diagram for attractive and for repulsive
interaction is deduced. For attraction, critical temperatures of faceting
transitions are found to depend on step density.
