Structure and relevant dimension of the Heisenberg model and applications to spin rings

For the diagonalization of the Hamilton matrix in the Heisenberg model relevant dimensions are determined depending on the applicable symmetries. Results an presented, birth, by general formulae in closed Form and by the respective numbers for a variety of special systems. In the case of cyclic symmetry, diagonalizations for Heisenberg spin rings are performed with the use of so-called magnon states. Analytically solvable cases of small spin rings are singled out and evaluated. (C) 2000 Elsevier Science B.V. All rights reserved.