  Employing numerical linked-cluster expansions (NLCEs) along with exact
diagonalizations of finite clusters with periodic boundary condition, we study
the energy, specific heat, entropy, and various susceptibilities of the
antiferromagnetic Heisenberg model on the checkerboard lattice. NLCEs, combined
with extrapolation techniques, allow us to access temperatures much lower than
those accessible to exact diagonalization and other series expansions. We find
that the high-temperature peak in specific heat decreases as the frustration
increases, consistent with the large amount of unquenched entropy in the region
around maximum classical frustration, where the nearest-neighbor and
next-nearest neighbor exchange interactions (J and J', respectively) have the
same strength, and with the formation of a second peak at lower temperatures.
The staggered susceptibility shows a change of character when J' increases
beyond 0.75J, implying the disappearance of the long-range antiferromagnetic
order at zero temperature. For J'=4J, in the limit of weakly coupled crossed
chains, we find large susceptibilities for stripe and Neel order with
Q=(pi/2,pi/2) at low temperatures with antiferromagnetic correlations along the
chains. Other magnetic and bond orderings, such as a plaquette valence-bond
solid and a crossed-dimer order suggested by previous studies, have also been
investigated.
