  Ultra-cold alkali atoms trapped in two distinct hyperfine states in an
external magnetic field can mimic magnetic systems of spin 1/2 particles. We
describe the spin-dependent effective interaction as a spin-spin interaction.
As a consequence of the zero-range, the interaction of spin 1/2 bosons can be
described as an Ising or, alternatively, as an XY-coupling. We calculated the
spin-spin interaction parameters as a function of the external magnetic field
in the Degenerate Internal State (DIS) approximation. We illustrate the
advantage of the spin-spin interaction form by mapping the system of N spin 1/2
bosons confined by a tight trapping potential on that of N spin 1/2 spins
coupled via an infinite range interaction.
