  Spin-crossover compounds, which are characterized by magnetic ions showing
low-spin and high-spin states at thermally accessible energies, are ubiquitous
in nature. We here focus on the effect of an exchange interaction on the
collective properties for the case of non-magnetic low-spin ions, which applies
to Fe(II) compounds. Monte Carlo simulations are used to study a
three-dimensional spin-crossover model for the full parameter range from
essentially pure high spin to essentially pure low spin. We find that as the
low-spin state becomes more favorable, the Curie temperature drops, the
universality class deviates from the three-dimensional Heisenberg class, and
the transition eventually changes to first order. A heat-bath algorithm that
grows or shrinks low-spin and high-spin domains is developed to handle the
first-order transition. When the ground state has low spin, a reentrant
magnetic transition is found in a broad parameter range. We also observe a
percolation transition of the high spins, which branches off the first-order
magnetic transition.
