Confinement in the q - state Potts field theory

The q-state Potts field theory describes the universality class associated to the spontaneous breaking of the permutation symmetry of q colors. In two dimensions it is defined up to q = 4 and exhibits duality and integrability away from critical temperature in absence of magnetic field. We show how, when a magnetic field is switched on, it provides the simplest model of confinement allowing for both mesons and baryons. Deconfined quarks (kinks) exist in a phase bounded by a first order transition on one side, and a second order transition on the other. The evolution of the mass spectrum with temperature and magnetic field is discussed.