  Motivated by recent experimental studies of Hg and Pb monolayers on Cu(001)
we introduce a zero temperature model of a monolayer adsorbed on a square
substrate. Lennard-Jones potentials are used to describe the interaction
between pairs of adlayer-adlayer and adlayer-substrate atoms. We study a
special case in which the monolayer atoms form a perfect square structure and
the lattice constant, position and orientation with respect to the substrate
can vary to minimize the energy. We introduce a rule based on the Farey tree
construction to generate systematically the most energetically favored phases
and use it to calculate the phase diagram in this model.
