Origin of mean-field behavior in an elastic Ising model

We derived an effective Hamiltonian for a commonly-used model of spin-crossover compounds in particlar and lattice-mismatched solids generally. In doing so, we showed how the effective interactions that arise from integrating out mechanical degrees of freedom yield classical (mean-field) critical behavior. We then demonstrated that simple mean-field theories based on these effective interactions predict a range of thermodynamic and kinetic properties that closely agree with Monte Carlo simulations of the model.