Spin-one Heisenberg ferromagnet with biquadratic exchange

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Abstract
The statistical mechanics of uniaxial S=1 ferromagnets with biquadratic exchange is considered in both ferromagnetic and quadrupolar phases using the standard basis-operator method proposed by Haley and Erdos (1972). In the random phase approximation, the collective excitation spectrum and thermodynamical properties of the system are discussed in detail, with stress laid on the role of kinematic restrictions with regard to the operators of the standard basis. The results are compared with those of molecular field theory, constant coupling approximation, and the high-temperature series expansion method. The problem of stability of the quadrupolar ordering is also considered by having recourse to the nonrelativistic analogue Goldstone theorem.