Neel Temperature of Quasi-Low-Dimensional Heisenberg Antiferromagnets

The N'eel temperature, $T_{\mathrm{N}}$, of quasi-one- and quasi-two-dimensional antiferromagnetic Heisenberg models on a cubic lattice is calculated by Monte Carlo simulations as a function of inter-chain (inter-layer) to intra-chain (intra-layer) coupling $J^{\mathrm{\prime }}\mathrm{/}J$ down to $J^{\mathrm{\prime }}\mathrm{/}J\simeq {10}^{-3}$. We find that $T_{\mathrm{N}}$ obeys a modified random-phase approximation-like relation for small $J^{\mathrm{\prime }}\mathrm{/}J$ with an effective universal renormalized coordination number, independent of the size of the spin. Empirical formulae describing $T_{\mathrm{N}}$ for a wide range of $J^{\mathrm{\prime }}$ and useful for the analysis of experimental measurements are presented.