Directional Ordering of Fluctuations in a Two-dimensional Compass Model

TL;DR

This paper investigates a classical two-dimensional orbital model with directional interactions, revealing entropy-driven ordering and a phase transition in the Ising universality class through simulations and exact mapping.

Contribution

It introduces a classical 2D compass model demonstrating entropy-stabilized directional orbital ordering and characterizes its phase transition.

Findings

Partial orbital ordering due to directional fluctuations

Entropy gap stabilizes ordered phase at low temperatures

Transition belongs to the Ising universality class

Abstract

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.