Orbital order in classical models of transition-metal compoundsZ. Nussinov1, M. Biskup2, L. Chayes2 and J. van den Brink3
1 Theoretical Division, Los Alamos National Laboratory - Los Alamos, NM 87545, USA
2 Department of Mathematics, UCLA - Los Angeles CA 90095-1555, USA
3 Lorentz Institute for Theoretical Physics, Universiteit Leiden Postbus 9506, NL-2300 RA Leiden, The Netherlands
(Received 15 March 2004; accepted in final form 2 July 2004)
We study the classical 120 degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We demonstrate that at low temperatures these models exhibit a long-range order which arises via an "order by disorder" mechanism. This strongly indicates that there is orbital ordering in the quantum version of these models, notwithstanding recent rigorous results on the absence of spin order in these systems.
71.20.Be - Transition metals and alloys.
05.70.Fh - Phase transitions: general studies.
75.30.Ds - Spin waves.
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