RENORMALIZATION-GROUP TRANSFORMATIONS FOR SPIN SYSTEMS

We develop a systematic approach to perform real space renormalization group transformations of the ''decimation type'' using perturbation t heory. This type of transformations beyond d = 1 is non-trivial even f or the Gaussian model on the lattice, Such a transformation is constru cted on a hypercubic lattice in arbitrary dimensions, and perturbation theory for spin models is developed around it. We check the formalism on the solvable O(N) symmetric Heisenberg chain. The decimations are especially useful to study models undergoing a continuous phase transi tion at zero temperature, Results for one class of such models, the D = 2 O(N) symmetric classical spins (N greater than or equal to 3) for decimation with scale factor eta = 2 (when one quarter of the points i s left), are presented.