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The N\'eel temperature, $T_{\rm N}$, of quasi-one- and quasi-two-dimensionalantiferromagnetic Heisenberg models on a cubic lattice is calculated by MonteCarlo simulations as a function of inter-chain (inter-layer) to intra-chain(intra-layer) coupling $J'/J$ down to $J'/J\simeq 10^{-3}$. We find that$T_{\rm N}$ obeys a modified random-phase approximation-like relation for small$J'/J$ with an effective universal renormalized coordination number,independent of the size of the spin. Empirical formulae describing $T_{\rm N}$for a wide range of $J'$ and useful for the analysis of experimentalmeasurements are presented.Comment: 4 pages, 4 figures, to be published in Phys. Rev. Let

Néel Temperature of Quasi-Low-Dimensional Heisenberg Antiferromagnets