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A two-component spin system with cubic anisotropy sufficiently large to remove the renormalization-group fixed point is investigated using differential recursion relations. An explicit free energy is constructed and it is verified explicitly that the loss of a fixed point corresponds to a first-order transition to the system's ordered state. A tricritical point is located and scaling properties of the first-order transition are investigated close to it.
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Joseph Rudnick (1978) studied this question.
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