A simple way of understanding some exact results on critical phenomena in non-homogeneous and finite Ising systems (Ferrell's continuum approximation) I

In generalizing a continuum approximation suggested by Ferrell for a spatially homogeneous Ising model, some results of earlier, exact calculations concerning the critical thermodynamics of certain spatially non-homogeneous 2d Ising systems are reproduced in a more transparent way, and the typical details of their dependence on the parameters of the inhomogeneity (amplitude, wavelength) are interpreted in terms of a simple physical picture.