Thermodynamics of an extended Fredrickson-Andersen model

We describe an extension of the Fredrickson-Andersen model (or n-spin facilitated kinetic Ising model) which exhibits a transition similar to a glass transition. Our extension incorporates long-range effects. Exact or numerically accurate results are obtained only for one dimension, but most conclusions apply more generally. The model exhibits a discontinuous drop in the specific heat as it is cooled through the transition temperature. This leads to an excess internal energy and a residual entropy at zero temperature. The disorder associated with the residual entropy can be seen in diffuse scattering which is characteristic of disordered systems.