Monte Carlo simulations of a compressible Ising ferromagnet at constant volume

Compressible Ising models have long been of interest because of the question of how the transition is influenced by elastic degrees of freedom. A careful Monte Carlo study showed, somewhat surprisingly, that an Ising ferromagnet at constant pressure had mean field critical behavior. Subsequently, a theoretical investigation predicted that the effect of elastic interactions depends upon whether the pressure or the volume is held fixed. We have now performed extensive Monte Carlo simulations of a compressible Ising ferromagnet at constant volume and determined the phase diagram as a function of applied magnetic field. In contrast to theoretical predictions, we find a single phase boundary that is first order everywhere except at single point where dT/dH=0. Unusual, slab-like structures are found in the “ordered” phase, and visualization played a crucial role in elucidating the physical behavior.