  We study equilibrium properties of a system of particles in two dimensions,
interacting with pair and three body potentials, which undergoes a structural
transition from a square to a rhombic lattice and thus constitutes a simple
model for a generic tetragonal to orthorhombic transition. We aim at an
intermediate level of description lying in-between that of coarse grained
elastic strain hamiltonians and microscopic ab-initio approaches. Macroscopic
thermodynamic properties and phase diagram at zero and finite temperatures as a
function of the density and the relative strengths of the pair and three body
energies are obtained using lattice sums, an approximate `cell-model' theory
and molecular dynamics simulations in the NVT ensemble. We propose that this
model solid can be used as a test bed for studies of statics and dynamics of
structural transitions.
