Surface effects in quantum spin chains

Chains of quantum spins with open ends and isotropic Heisenberg exchange are studied. By diagonalizing the Hamiltonian for chains of finite length N and obtaining all the energy eigenvalues, the magnetic susceptibility X, the specific heat C, and the partition function Z can be calculated exactly for these chains. The high-temperature series expansions of these are then evaluated. For X and C, it is found that the terms in the series consist of three parts. One is the normal high-T series already known in great detail for the N --> infinity ring (chain with periodic boundary conditions). The other two consist of a 'surface' term and a correction term of order (1/T)(N). The surface term is found as a series up to and including (1/T)(8) for spin S = 1/2 and 1. Simple Pade approximant formulae are given to extend the range of validity below T = 1.