Critical interactions for the triangular spin-sIsing model by a spin-restructuring transformation

A transformation is constructed which maps the spin-$s$ Ising model onto a spin-½ Ising model with furtherneighbor and many-site interactions. Renormalization-group methods may thus be applied directly to the spin-$s$ problem by prefacing the usual sequence of position-space rescaling transformations with this spin-restructuring transformation. We demonstrate the method by calculating the critical interactions (i.e., the inverse critical temperatures) of the spin-$s$ Ising model on the triangular lattice, using the recent results of Niemeijer and van Leeuwen for the critical subspace of the corresponding spin-½ Ising model. Our evaluations agree very well with recent series data.