Band-filling driven crossover from ferro to antiferromagnetic order in Ising lattices decorated by quantum dimers

We introduce an exactly solvable model of hybrid spin lattices having nodal Ising spins and decorating quantum dimers with a varying band-filling. The kinetic energy of the decorating electrons induces an effective coupling between nodal Ising spins. We provide the full phase diagram in square and cubic lattices as a function of the band-filling showing reentrant phases and a crossover from ferro to antiferromagnetic ordering. The dependence of the effective ferro and antiferromagnetic couplings on the kinetic energy of decorating electrons, as well as their distinct sensitivity to thermal fluctuations, are shown to govern the main features of the reentrant phases.