Phase diagrams of liquid helium mixtures and metamagnets: Experiment and mean field theory

The phase behavior at low temperature, in particular the critical and tricritical properties, of liquid ³He⁴He mixtures and certain types of metamagnets — a class of highly anisotropic antiferromagnets, such as FeCl₂ etc. — is investigated. Since both systems exhibit two successive phase transitions, one of which is a λ-type of transition while the other is a first order transition, special attention is given to the similarity in the behavior of the two systems. In part A first the experimental and earlier theoretical work are briefly reviewed. Then the phase behavior of each system is calculated on the basis of a simple model treated in mean field approximation. The results obtained are in general qualitative agreement with experiment. For the helium mixtures an isotopic mixture of hard-spheres following Fermi and Bose statistics is used, while for the metamagnet a two sublattice spin $\text{1}\text{2}$ Ising model with nearest neighbor and next-nearest neighbor interactions is employed. A simple physical argument for the analogous behavior of the two models is given. In part B, in an attempt to obtain a deeper understanding of the similarity of the two systems, the Hamiltonians of the two models are extended to include symmetry breaking fields: a particle source field for the helium mixtures and a staggered magnetic field for the metamagnet. The phase diagrams and critical behavior of the two models in an extended thermodynamic space that includes the symmetry breaking fields are discussed in mean field theory.We find that although the two models (treated in the mean field approximation) are very similar, there are differences near T = 0°K and in some of the critical exponents.