Finite-lattice approach to the O(2) and O(3) models in 1 + 1 dimensions and the (2+1)-dimensional Ising model

Abstract
The Lanczos scheme for finding low-lying eigenvalues of a sparse matrix of large dimension is applied to solving the Hamiltonian formulation for the O(2) and O(3) spin systems in 1 + 1 dimensions and the Ising model in 2 + 1 dimensions. We confirm results obtained for these models in other ways. The new method is shown to be competitive with the other methods available for solving these problems.