Exact analytical partition function and energy levels for a Heisenberg ring of N=6 spin 1/2 sites

Using a method which combines reduction due to translational symmetry and elimination of degenerate states from smaller subspaces, the 64 x 64 Hamiltonian matrix of a Heisenberg ring of N = 6 spin 1/2 atoms can be reduced to submatrices that are no larger than 3 x 3. This reduction makes possible the calculation of the exact eigenenergies E(k) of the system and subsequently the derivation of the partition function in an exact analytical form. The results are in perfect agreement with those obtained numerically by other authors. (C) 1998 Elsevier Science B.V. All rights reserved.