1304.2108 (Helen Au-Yang et al.)

Criticality in Alternating Layered Ising Models : I. Effects of
connectivity and proximity    [PDF]

Helen Au-Yang, Michael E. Fisher

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 coworkers in experiments on confined superfluid helium. Explicitly, we demonstrate that finite-size scaling holds in the vicinity of the upper limiting critical point $T_{1c}$ ($\propto J_1/k_B$) and close to the corresponding lower critical limit $T_{2c}$ ($\propto J_2/k_B$) when $m_1$ and $m_2$ increase. However, the residual {\it enhancement}, defined via appropriate subtractions of leading contributions from the total specific heat, is dominated (away from $T_{1c}$) by a decay factor $1/(m_1+m_2)$ arising from the {\it seams} (or boundaries) separating the strips; close to $T_{1c}$ the decay is slower by a factor $\ln(m_1/m_0)$.

View original: http://arxiv.org/abs/1304.2108