Role of detailed balance on the phase diagram of frustrated systems; the modified ANNNI model

We study the effect of removing detailed balance from the axial next-nearest-neighbour Ising (ANNNI) model on its phase diagram. Although the concepts of free energy or Gibbsian thermodynamical equilibrium no longer apply, we find numerically that the phase diagram is preserved even when the interactions are completely unidirectional. We also find that the value of the multiphase point varies with the degree of asymmetry in the rules.