Antiferromagnetic ordering in the three-state Potts model

The three-state Potts model on a triangular lattice with nearest neighbour interaction K is studied. Using a simple position-space renormalisation group transformation it is found that, in addition to the usual continuous transition to the ferromagnetic state which occurs for positive K, a continuous transition to an antiferromagnetic state occurs for negative K. The transformation introduces a three-spin interaction. In the space of these two interactions, the lines of ferromagnetic and antiferromagnetic transitions meet at a bicritical point. These results differ from those predicted by Landau theory.