Sublattice renormalization transformations for spin 12 models on a square lattice

Ising-like models on a square lattice are studied by real space renormalization transformations in which the cells are confined to sublattices. A general class of transformations is discussed which maps all ground states that are invariant under translation over n lattice constants onto themselves. Numerical results on the simplest non-trivial case of n = 2 are given in the lowest approximation involving 16 spins on a square lattice with periodic boundary conditions. The parameter space includes first and second neighbor couplings, four-spin coupling, magnetic field and three-spin coupling. A rich critical structure including seven different fixed points is found. For the calculation of eigenvalues three additional couplings are included: a second neighbor interaction alternating in sign between the two main sublattices, a staggered field, and a staggered three-spin coupling.