Criticality in Alternating Layered Ising Models: II. Exact Scaling Theory

TL;DR

This paper provides exact scaling theory for the specific heat in alternating layered Ising models, confirming previous graphical results and showing the exponential decay of the logarithmic singularity at the critical point with increasing strip width.

Contribution

It offers a rigorous theoretical analysis and asymptotics that support earlier graphical findings on the critical behavior of layered Ising models.

Findings

Logarithmic singularity vanishes exponentially with strip width

Finite-size scaling holds near the critical point

Exact asymptotics support graphical results

Abstract

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 coworkers. 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.