New Methods for Hamiltonian Lattice Theories.

A variety of position space renormalization group techniques are applied to the Hamiltonian formulation of the Z(2), Z(3), O(2) and O(3) models in 1 + 1 dimensions and to the 2 + 1 dimensional Ising model. The techniques are shown to be capable of producing qualitatively correct but quanitatively inaccurate results. A second sheme, based on the Lanczos method for finding low-lying eigenvalues of a sparse symmetric matrix of large dimension, is applied to solving the finite lattice version of the same models. This scheme is supplemented with a new scaling technique to extrapolate the results to the infinite lattice limit. The method is shown to be competitive with the other methods available for solving these problems.