Critical behaviour of fully frustrated Potts models

A numerical transfer matrix calculation is presented for two fully frustrated three-state Potts models on the square lattice: the Potts piled-up-domino model and the Potts zig-zag model. The ground state entropies and phase diagrams are found. The Potts piled-up-domino model displays a finite-temperature transition when the frustration effects are maximal, and displays re-entrant behaviour, in contrast to the Ising model equivalent. The ground-state entropy per spin is larger than in the Ising equivalent. The Potts zig-zag model displays the same qualitative behaviour as its Ising counterpart, and the ground-state entropy per spin is the same in the Potts and Ising cases.