Marginal dimensions of the Potts model with invisible states

Abstract

We reconsider the mean-field Potts model with q interacting and r non-interacting (invisible) states. The model was recently introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where the Zq-symmetry is spontaneously broken. We analyse the marginal dimensions of the model, i.e., the value of r at which the order of the phase transition changes. In the q = 2 case, we determine that value to be there is a second-order phase transition there when and a first-order one at . We also analyse the region and show that the change from second to first order there is manifest through a new mechanism involving two marginal values of r. The q = 1 limit gives bond percolation. Above the lower value rc1, the order parameters exhibit discontinuities at temperature below a critical value tc. The larger value rc2 marks the point at which the phase transition at tc changes from second to first order. Thus, for , the transition at tc remains second order while at the system undergoes a first order phase transition. As r increases further, increases, bringing the discontinuity closer to tc. Finally, when r exceeds rc2 coincides with tc and the phase transition becomes first order. This new mechanism indicates how the discontinuity characteristic of first order phase transitions emerges.