The Ising Model and Real Magnetic Materials

The factors that make certain magnetic materials behave similarly to corresponding Ising models are reviewed. Examples of extensively studied materials include Dy(C2H5SO4)3.9H2) (DyES), Dy3Al5O12 (DyAlG), DyPO4, Dy2Ti2O7, LiTbF4, K2CoF4, and Rb2CoF4. Various comparisons between theory and experiment for these materials are examined. The agreement is found to be generally very good, even when there are clear di erences between the ideal Ising model and the real materials. In a number of experiments behavior has been observed that requires extensions of the usual Ising model. These include the e ects of long range magnetic dipole interactions, competing interaction e ects in eld-induced phase transitions, induced staggered eld e ects and frustration e ects, and dynamic e ects. The results show that the Ising model and real magnetic materials have provided an unusually rich and productive eld for the interaction between theory and experiment over the past 40 years.