Monte Carlo study of the critical properties of the three-dimensional 120 degrees model

We report on large scale finite-temperature Monte Carlo simulations of the prototypical classical 120 degrees or e(g) model for orbital ordering on the simple cubic lattice in three dimensions. Our study reveals a continuous phase transition to an orbitally ordered phase with unusual critical properties compared to standard magnetism. While the correlation length exponent nu approximate to 0.665 is close to the 3D XY value, the exponent eta approximate to 0.15 differs substantially from O(N) values. Our results are corroborated by simulation results from a discrete e(g)-clock model that we have defined.