  We have used the stochastic series expansion (SSE) quantum Monte Carlo (QMC)
method to study the three-dimensional (3D) antiferromagnetic Heisenberg model
on cubic lattices with in-plane coupling J and varying inter-plane coupling
J_perp < J. The specific heat curves exhibit a 3D ordering peak as well as a
broad maximum arising from short-range 2D order. For J_perp << J, there is a
clear separation of the two peaks. In the simulations, the contributions to the
total specific heat from the ordering across and within the layers can be
separated, and this enables us to study in detail the 3D peak around T_c (which
otherwise typically is dominated by statistical noise). We find that the peak
height decreases with decreasing J_perp, becoming nearly linear below J_perp =
0.2J. The relevance of these results to the lack of observed specific heat
anomaly at the ordering transition of some quasi-2D antiferromagnets is
discussed.
