We use a quantum Monte Carlo method to calculate the Neel temperature T_N of weakly coupled S=1/2 Heisenberg antiferromagnetic layers consisting of coupled ladders. This system can be tuned to different two-dimensional scaling regimes for T > T_N. In a single-layer mean-field theory, chi_s^{2D}(T_N)=(z_2J)^{-1}, where chi_s^{2D} is the exact staggered susceptibility of an isolated layer, J the inter-layer coupling, and z_2=2 the layer coordination number. With a renormalized z_2, we find that this relationship applies not only in the renormalized-classical regime, as shown previously, but also in the quantum-critical regime and part of the quantum-disordered regime. The renormalization is nearly constant; k_2 ~ 0.65-0.70. We also study other universal scaling functions.
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