Turkish Journal of Physics






The phenomenon of order by disorder in frustrated magnetic systems is reviewed. Disorder (thermal or quantum fluctuations) may sometimes give rise to long range ordering in systems with frustration, where one must often consider the selection among classically degenerate ground states which are not equivalent by any symmetry. The lowest order effects of quantum fluctuations in such frustrated systems usually resolves the continues degeneracy of the ground state manifold into discrete Ising--type degeneracy. A unique ground state selection out of this Ising degenerate manifold then occurs due to higher order effects of quantum fluctuations. For systems such as face-centered cubic and body-centered tetragonal antiferromagnets where the number of Ising parameters to describe the ground state manifold is not macroscopic, we show that quantum fluctuations choose a unique ground state at the first order in 1/S. However for kagom'{e} antiferromagnet where the ground state manifold is macroscopic, a unique ground state selection can only occur at high orders in 1/S. We show that the main effect of the zero--point fluctuations is at small wavevector and can be well modeled by an effective biquadratic interaction of the form \Delta E_{Q}^{eff} = -\frac{1}{2}Q \sum_{i,j} ({\bf S}_{i} \cdot {\bf S_{j} )^{2}/S^{3} This interaction opens a quantum spin gap by splitting the classical zero--energy modes into one zero--energy Goldstone mode and nonzero energy modes. We calculate this quantum gap at relative order 1/S using the standard Hartree decoupling of the higher order interaction terms.

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