Abstract
An exchange-coupled Ising system of doubly degenerate four-level ions, with uniaxial crystal-field single-ion anisotropy, is investigated. Using the technique of thermodynamic Green functions the system free energy is calculated within the random-phase approximation (RPA). By consideration of an appropriate three-level system, previously analyzed by Capel, the RPA is shown to yield identical results to the Bragg-Williams molecular field approximation. Landau's theory of phase transitions is used to study regions of first and second order phase transitions. In contrast to the three-level system, it is found that the four-level system may have isolated continuous transitions occurring at nonzero magnetization.
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