Exactly solved dynamics for an infinite-range spin system

It is well known that the dynamical evolution of a system of N spins can be viewed as a walk along the edges of an N-dimensional hypercube. I use this correspondence in an infinite-range spin system to derive a diffusion equation for the magnetization. The diffusion equation then leads to an ordinary differential equation that describes the time evolution of the magnetization for any given initial condition, and it is used to derive both static and dynamic properties of the spin system.