MAPPING OF p-STATE SYMMETRIC VERTEX MODEL ON THE HONEYCOMB LATTICE ONTO ITS ISING-SPIN COUNTERPART

The mapping which produces a path between the p-state symmetric vertex model and the Ising model with spin $\frac{p -1}{2}$ on the honeycomb lattice is constructed. The mapping construction is based on a combination of decoration and gauge transformations. The formulation enables one to find the manifold in the vertex weights parameter space on which the mapping can be performed and to derive dual relations among the model parameters as well as the free energies of related symmetric vertex and Ising models. The extension of the mapping to arbitrary lattice coordination is outlined.