Monte Carlo studies of critical phase behaviors of compressible Ising models

Monte Carlo simulations of two different compressible Ising models are presented. One is an elastic, antiferromagnetic Ising model on a distortable diamond net at constant pressure. Spins interact via a Stillinger-Weber-like potential, and data were obtained over a wide range of temperature and magnetic field. The phase boundary is a line of 2nd order transitions between ordered and disordered states. Our analysis shows that this model shares the same critical exponents with the rigid 3-D simple-cubic Ising model, despite the difference in structure and interactions. This implies that they both belong to the same universality class. We also present a thorough examination of the models elastic degrees of freedom. The other model is a stacked triangular lattice where spins interact via Lennard-Jones potential. Thismodel features adjustable elasticity. However, analysis shows that the phase transition also belongs to the rigid 3-D simple-cubic Ising universality. Both results contradict theoretical predictions.