Order by Disorder and Topology in Frustrated Magnetic Systems

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The phenomenon of order by disorder in frustrated magnetic systems is reviewed. Thermal, quantum, and even quenched noise may sometimes increase ordering in systems where energetics ensure a nontrivially degenerate classical ground state. In systems where the number of variables parametrizing the manifold of degenerate ground states is not macroscopic, fluctuations may remove the degeneracy and reduce the symmetry to that of the Ising model. We concentrate on the kagomé antiferromagnet, whose manifold of ground states has a macroscopic number of degrees of freedom. In this system, thermal fluctuations around ground states lead to entropically driven local spin nematic order at low T. The fluctuations are so strong that no single state or finite set of states is selected. We derive an effective Hamiltonian, giving a description in terms of the variables of a fluctuating surface. A novel phenomenon, that of quasi-nonergodicity, arising in a perfectly frustrated lattice, is briefly discussed.