Directional Ordering of Fluctuations in a Two-dimensional Compass Model
  In the Mott insulating phase of the transition metal oxides, the effective orbital-orbital interaction is directional both in the orbital space and in the real space. We discuss a classical realization of directional coupling in two dimensions. Despite extensive degeneracy of the ground state, the model exhibits partial orbital ordering in the form of directional ordering of fluctuations at low temperatures stabilized by an entropy gap. Transition to the disordered phase is shown to be in the Ising universality class through exact mapping and multicanonical Monte Carlo simulations. 
Anup Mishra, Michael Ma, Fu-Chun Zhang, Siegfried Guertler, Lei-Han   Tang, and Shaolong Wan