At finite imaginary values of the chemical potential, QCD is free of the sign problem. Moreover, at
high temperatures the partition function exhibits a new symmetry (the Roberge-Weiss symmetry)
connecting phases with different orientations of the Polyakov loop, and the corresponding phase
transitions between these. In this contribution we investigate the perturbative one-loop effective
potential for the Polyakov loop in the presence of imaginary isospin as well as baryon chemical
potentials. This leads to a novel phase diagram, which reveals an interesting insight about the
rich phase structure of the system and the center symmetry breaking. We check the perturbative
results using direct lattice simulations.