Critical exponents of the U(n) vector spin glasses

The critical exponents of the classical spin glasses with O(m − 2n)⊗U(n) symmetry are obtained to order 2 of the -expansion around six dimensions, where = 6 − d. This new unitary symmetry is realized in the m-vector (m ≥ 2) spin glasses with anisotropic quenched random Dzyaloshinskii-Moriya (DM) interaction. Such a random DM interaction with n correlated couplings leads to critical exponents which are different from those of any isotropic m-vector spin glass and thus belong to new universality classes.