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The critical behaviour of an m-component (m>or=2) spin glass in a magnetic field is studied near six dimensions. The critical behavior associated with the freezing of the transverse degrees of freedom (Gabay-Toulouse transition) is shown to be identical, to all orders in epsilon =6-d, to that of an isotropic (m-1)-component spin glass in zero field.
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Moore et al. (1982) studied this question.
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