 The restriction on vertex states is that the product of four edges at a vertex is 1; this automatically holds for Ising 'edges'.Each formula_56 configuration then corresponds to a unique formula_54, formula_55 configuration, whereas each formula_54, formula_55 configuration gives two choices of formula_56 configurations.Equating general forms of Boltzmann weights for each vertex formula_4, the following relations between the formula_5 and formula_49, formula_50, formula_51, formula_52, formula_53 define the correspondence between the lattice models