Geometrization of spin systems using cycle expansions

Abstract

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.