Differential real space renormalization: The linear Ising chain

The differential real space renormalization method, recently introduced by Hillhorst et al., is applied to the linear Ising chain. It is shown that chains with spatially homogeneous as well as inhomogeneous or quenched random interactions can be treated. For the first two cases the free energy is computed by renormalization. The discussion includes also the case with a magnetic field, higher order interactions and the behavior of correlation functions under renormalization.