Unveiling the Nature of Three-Dimensional Orbital Ordering Transitions: The Case of e(g) and t(2g) Models on the Cubic Lattice

We perform large scale finite-temperature Monte Carlo simulations of the classical e(g) and t(2g) orbital models on the simple cubic lattice in three dimensions. The e(g) model displays a continuous phase transition to an orbitally ordered phase. While the correlation length exponent nu approximate to 0.66(1) is close to the 3D XY value, the exponent eta approximate to 0.15(1)differs substantially from O(N) values. At T-c a U(1) symmetry emerges, which persists for T < T-c below a crossover length scaling as Lambda similar to xi(a), with an unusually small a approximate to 1.3. Finally, for the t(2g) model we find a first order transition into a low-temperature lattice-nematic phase without orbital order.