An algorithm to obtain exact eigenvalues and eigenstates of the arbitrary spin Ising Hamiltonian in d dimensions

The Hamiltonian of the Ising model in d dimensions has been analysed using unitary transformations and combinatorics. We have been able to obtain clos ed formulas for the eigenvalues of the Ising Hamiltonian in an arbitrary nu mber of dimensions. Furthermore, generalisations to a higher number of spin components on each site are possible within this method. We have made nume rical comparisons with the partition function from the earlier analytical e xpressions known in the literature for one and two-dimensional cases and fo und complete agreement. (C) 2001 Elsevier Science B.V. All rights reserved.