Existence of long-range orbital order in a two-dimensional orbital-only model

In the present paper, by applying the reflection positivity method due to Dyson, Lieb, and Simon, we rigorously establish the existence of an antiferromagneticlike transverse orbital long-range order in the so-called two-dimensional 120 degrees model at zero temperature. Our result shows that, although this model has a built-in frustration mechanism which disfavors long-range orbital order, its effect is actually not sufficiently strong to destroy the existence of such ordering in the system.