Ising model,crossing bonds and four-spin interactions

The Ising model on a square lattice is investigated in the presence of additional crossing bonds and four-spin interaction. Under some restrictions, exact transformation of a four-spin square to a square with central decorating spin interacting with spins on four surrounding vertices is possible. The transformation leads to ordinary or standard bond decorated Ising models, which permits exact determination of the critical temperature for some particular values of the interaction parameters even in the presence of magnetic field acting on all sites of the lattice. (author)