First-order directional ordering transition in the three-dimensional compass model

We study the low-temperature properties of the classical three-dimensional compass or $t_{2g}$ orbital model on simple-cubic lattices by means of comprehensive large-scale Monte Carlo simulations. Our numerical results give evidence for a directionally ordered phase that is reached via a first-order transition at the temperature $T_0 = 0.098328(3) J / k_{\mathrm{B}}$. To obtain our results we employ local and cluster update algorithms, parallel tempering and multiple histogram reweighting as well as model-specific screw-periodic boundary conditions, which help counteract severe finite-size effects.