Monte Carlo simulations of lattice models with finite subgroups of SU(3) as gauge groups

A Monte Carlo study of four-dimensional gauge theory on five crystal-like subgroups of SU(3) is carried out using the Wilson action. All these models are found to have a first-order freezing (order-disorder) phase transition due to the discrete nature of the groups. This transition occurs before the continuum, scaling limit is approached. Hence, it is not possible to use any of these groups to approximate the continuum limit of the SU(3) gauge theory with the Wilson action.