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

Abstract

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.

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

References in corpus (3)

• Order by disorder, without order, in a two-dimensional spin system with O(2) symmetry
• Central limit theorems for the large-spin asymptotics of quantum spins
• The large-spin asymptotics of the ferromagnetic XXZ chain

Cited by in corpus (14)

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• Doubly degenerate orbital system in honeycomb lattice: implication of orbital state in layered iron oxide
• Quantum phase transitions in exactly solvable one-dimensional compass models
• Exact Universal Chaos, Speed Limit, Acceleration, Planckian Transport Coefficient, "Collapse" to equilibrium, and Other Bounds in Thermal Quantum Systems
• Orbital order driven quantum criticality
• Intermediate Symmetries In Electronic Systems: Dimensional Reduction, Order Out Of Disorder, Dualities, And Fractionalization
• Fluctuation control of non-thermal orbital order
• Unveiling the nature of three dimensional orbital ordering transitions: the case of $e_g$ and $t_{2g}$ models on the cubic lattice
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• Nonthermal order by disorder