The critical behaviour of linear Phi 4 models with global symmetry O(N)*O(M) and U(N)*U(M) is studied at one-loop order in 4- epsilon dimensions. Applications to physical systems include achiral and chiral double-strand polymers, when N=M=0. There exist infrared stables fixed points only if N and M are sufficiently small. Some special cases of interest include (1) O(-2)*O(1) and U(-1)*U(1) which have classical exponents, (2) O(1)*O(1) and O(-2)*O(-2) (for example) which exhibit a 'merging' of critical exponents, (3) M finite, N to infinity which is also calculable in a 1/N expansion.
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Pisarski et al. (1981) studied this question.
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