Universal scaling of the Néel temperature of near-quantum-critical quasi-two-dimensional Heisenberg antiferromagnets

We use a quantum Monte Carlo method to calculate the N\'eel temperature TN 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>TN. In a single-layer mean-field theory, χₛ2D(TN)=(z₂J^')^-1, where χₛ2D is the exact staggered susceptibility of an isolated layer, J^' the interlayer coupling, and z₂=2 the layer coordination number. With a renormalized z₂, z₂→k₂z, 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; k₂≈0.65-0.70. We also study other universal scaling functions.