Phase transitions and local minima of the action

We present evidence that non-trivial, non-degenerate local minima of the one-plaquette action in 4-dimensional lattice gauge theories with continuous gauge groups, give rise to a line of first-order “discreteness” phase transitions, persisting down to the region where the non-trivial minima become unstable. We illustrate this mechanism by analysing an extended model, involving the traces in the fundamental and six representation of SU(3), in which neither the topology, nor the group theoretic properties of the centre seem to play any role.