A classical Heisenberg Hamiltonian, to which is added single-ion anisotropy and antisymmetric Dzialoshinsky-Moriya interactions is studied with use of Wilson theory. The phase diagram is obtained; it consists of ferromagnetic, spiral, and ferromagnetic-spiral regions, with critical exponents that are Ising-like, xy-like, and Heisenberg-like, respectively. These results lead to the conclusion that breaking of exchange symmetry does not change the nature of the phase transition. Crossover behavior is also discussed.
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Luke L. Liu (1973) studied this question.
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