The molecular-field approximation (MFA) and the random-phase approximation (RPA) are shown to be unreliable in predicting the types of order in cubic Heisenberg magnets that include second-neighbor exchange. Anomalies in the Pad\'e-approximant critical temperatures are found and traced to instabilities in the RPA and MFA. These instabilities lead to new types of order involving canted and perpendicular alignment of the spins.
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Robert H. Swendsen (1974) studied this question.
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