Orbital ordering in transition-metal compounds: I. The 120-degree model

Details Orbital ordering in transition-metal compounds: I. The 120-degree model Orbital ordering in transition-metal compounds: I. The 120-degree model

2003-09-30

arxiv.org/abs/cond-mat/0309691v3

Commun. Math. Phys. 255 (2005), no. 2, 253-292

Physics

Condensed Matter

Statistical Mechanics

40 pages, 1 eps fig; a revised version correcting a bunch of small errors

Scientific paper

10.1007/s00220-004-1272-7

We study the classical version of the 120-degree model. This is an attractive nearest-neighbor system in three dimensions with XY (rotor) spins and interaction such that only a particular projection of the spins gets coupled in each coordinate direction. Although the Hamiltonian has only discrete symmetries, it turns out that every constant field is a ground state. Employing a combination of spin-wave and contour arguments we establish the existence of long-range order at low temperatures. This suggests a mechanism for a type of ordering in certain models of transition-metal compounds where the very existence of long-range order has heretofore been a matter of some controversy.

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