  We present evidence that crystalline Sr_2Cu(PO_4)_2 is a nearly perfect
one-dimensional (1D) spin-1/2 anti-ferromagnetic Heisenberg model (AHM) chain
compound with nearest neighbor only exchange. We undertake a broad theoretical
study of the magnetic properties of this compound using first principles (LDA,
LDA+U calculations), exact diagonalization and Bethe-ansatz methodologies to
decompose the individual magnetic contributions, quantify their effect, and fit
to experimental data. We calculate that the conditions of one-dimensionality
and short-ranged magnetic interactions are sufficiently fulfilled that Bethe's
analytical solution should be applicable, opening up the possibility to explore
effects beyond the infinite chain limit of the AHM Hamiltonian. We begin such
an exploration by examining some extrinsic effects such as impurities and
defects.
