Kinetic Ising Model of the Glass Transition

A graph theory of single-spin-flip kinetic Ising models is developed and applied to a class of spin models with strongly cooperative dynamics. Self-consistent approximations for the spin time correlation function are presented. One of the dynamical models exhibits a glass transition with no underlying thermodynamic singularity. The approximation for the time correlation function predicts a critical temperature, below which small fluctuations from equilibrium in the thermodynamic limit cannot relax in a finite amount of time.