Can local composition models combined with global renormalization group theory describe the phase transitions in ferromagnetic materials?

The phase transition and phase separation in ferromagnetic materials can be regarded as a special type of liquid-liquid phase transition, and are modeled in this work using four popular mean-field local composition models, including Margules, NRTL, Wilson and COSMO-SAC. While local composition models have been proven powerful for correlating liquid-liquid phase transitions in highly non-ideal liquid mixtures, their capability in predicting the phase behaviors of liquid mixtures based on given molecular interactions is not fully understood. In this work, the exact magnetization (or, equivalently the equilibrium composition) and the Curie temperature (or the upper critical solution temperature) of square-lattice systems are used to examine the predictive power of local composition models. We find that all four local composition models correctly predict the liquid-liquid phase boundary at low temperatures, but become increasingly less accurate at high temperature and overestimate the upper critical solution temperature, as documented in prior studies. The deficiency caused by mean-field approximation in local composition models is remedied by applying the global renormalization group theory (GRGT) to include long-range composition fluctuations, which is most important near the critical point. We find that the COSMO-SAC model can best describe the phase boundary of ferromagnetic materials while other local composition models show significant deviation from the exact solution near the critical point.