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.

Criticality in alternating layered Ising models. I. Effects of connectivity and proximity.

The specific heats of exactly solvable alternating layered planar Ising models with strips of width m_{1} lattice spacings and "strong" couplings J_{1} sandwiched between strips of width m_{2} and "weak" coupling J_{2}, have been studied numerically to investigate the effects of connectivity and proximity. We find that the enhancements of the specific heats of the strong layers and of the overall or "bulk" critical temperature T_{c}(J_{1},J_{2};m_{1},m_{2}) arising from the collective effects reflect the observations of Gasparini and co-workers in experiments on confined superfluid helium. Explicitly, we demonstrate that finite-size scaling holds in the vicinity of the upper limiting critical point T_{1c} (∝J_{1}/k_{B}) and close to the corresponding lower critical limit T_{2c} (∝J_{2}/k_{B}) when m_{1} and m_{2} increase.