Specific heat of quasi-two-dimensional antiferromagnetic Heisenberg models with varying interplanar couplings

We have used the stochastic series expansion quantum Monte Carlo method to study the three-dimensional (3D) antiferromagnetic Heisenberg model on cubic lattices with in-plane coupling J and varying interplane coupling $J_{\perp }<J.\mathrm{}$ The specific heat curves exhibit a 3D ordering peak as well as a broad maximum arising from short-range 2D order. For $J_{\perp }\ll J,$ 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 $J_{\perp }=0.2\mathrm{}J.\mathrm{}$ The relevance of these results to the lack of an observed specific-heat anomaly at the ordering transition of some quasi-2D antiferromagnets is discussed.