Effective Hamiltonians for state selection in Heisenberg antiferromagnets

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In frustrated antiferromagnets with isotropic exchange interactions, there is typically a manifold of degenerate classical ground states. This degeneracy is broken by the (free) energy of quantum or thermal fluctuations, or the uniform effects of bond disorder. We derive effective Hamiltonians to express each kind of selection effect, in both exact forms and convenient approximate forms. It is argued that biquadratic terms, representing the collinear-selecting effects of quantum fluctuations, should be included in classical simulations of large-S frustrated magnets at low temperatures