Dualities for Extended Potts Models Induced from the Percolation Problems of Block Elements

The Potts model is extended to include the case of block type many-body interaction. The dilute ferromagnet on the block lattice is discussed as an extended Potts model with layers of lattice by using the real replica method. As a new type of self-dual lattice, the overlap-block lattice consisting of a block lattice and its dual lattice, is shown to have a Potts model structure. The dualities for those extended Potts models are proved on the basis of equivalences of the models to the percolation problems.