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

TL;DR

This paper analyzes the classical 120-degree model in three dimensions, demonstrating long-range order at low temperatures, which provides insights into orbital ordering mechanisms in transition-metal compounds.

Contribution

It introduces a detailed analysis of the classical 120-degree model, revealing the existence of long-range order and proposing a mechanism relevant to transition-metal compounds.

Findings

Long-range order exists at low temperatures.

Every constant field is a ground state.

Provides a mechanism for ordering in transition-metal models.

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.