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 at
oms. We study a special case in which the monolayer atoms form a perfe
ct square structure and the lattice constant, position and orientation
with respect to the substrate can vary to minimize the energy. We int
roduce a rule based on the Farey tree construction to generate systema
tically the most energetically favored phases and use it to calculate
the phase diagram in this model.