  It is shown that a spin system with long range interactions can be converted
into a chaotic dynamical system that is differentiable and low-dimensional. The
thermodynamic limit of the spin system is then equivalent to studying the long
term behavior of the dynamical system. Cycle expansions of chaotic systems
(expansion of the Fredholm determinant) are then used to study the
thermodynamic limit. By considering the smooth dynamical system, it is possible
to converge to the thermodynamic limit faster than with transfer matrices.
