Criticality in alternating layered Ising models. II. Exact scaling theory

Part I of this article studied the specific heats of planar alternating layered Ising models with strips of strong coupling J_{1} sandwiched between strips of weak coupling J_{2}, to illustrate qualitatively the effects of connectivity, proximity, and enhancement in analogy to those seen in extensive experiments on superfluid helium by Gasparini and co-workers. It was demonstrated graphically that finite-size scaling descriptions hold in a variety of temperature regions including in the vicinity of the two specific heat maxima. Here we provide exact theoretical analyses and asymptotics of the specific heat that support and confirm the graphical findings. Specifically, at the overall or bulk critical point, the anticipated (and always present) logarithmic singularity is shown to vanish exponentially fast as the width of the stronger strips increases.