  A system of atoms connected by harmonic springs to their nearest neighbors on
a lattice is coupled to Ising spins that are in contact with a thermal bath and
evolve under Glauber dynamics. Assuming a nearest-neighbor antiferromagnetic
interaction between spins, we calculate analytically the equilibrium state. On
a one-dimensional attice, the system exhibits first and second order phase
transitions. The order parameters are the total magnetization and the number of
spin pairs in an antiferromagnetic configuration. On a hexagonal two
dimensional lattice, spins interact with their nearest-neighbors and
next-nearest-neighbors. Together with the coupling to atoms, these interactions
produce a complex behavior that is displayed on a phase diagram. There are:
ordered phases associated to ripples with atomic wavelength and
antiferromagnetic order, ordered phases associated to ripples with nanometer
wavelengths and ferromagnetic order, disordered glassy phases, and other phases
presenting stripes formed by different domains. These static phases are
discussed in relation to existing experiments and results for other models
found in the literature.
