Spontaneous breaking of translational invariance in one-dimensional stationary states on a ring

We consider a model in which positive and negative particles diffuse in an asymmetric, CP-invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent particles may swap positions. Monte Carlo simulations and analytic calculations suggest that the model has three phases; a 'pure' phase in which one has three pinned blocks of only positive, negative particles and vacancies, and in which translational invariance is spontaneously broken, a 'mixed' phase with a non-vanishing current in which the three blocks are positive, negative and neutral, and a disordered phase without blocks.