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The Neel temperature and sublattice magnetization for the stacked triangular-lattice antiferromagnet with a weak interlayer coupling

The quantum Heisenberg antiferromagnet on the stacked triangular lattice with the intralayer nearest-neighbor exchange interaction J and interlayer exchange J&#39; is considered within the non-linear $σ$-model with the use of the renormalization group (RG) approach. For J&#39; << J the asymptotic formula for the Neel temperature $T_{Neel}$ and sublattice magnetization are obtained. RG turns out to be insufficient to describe experimental data since it does not take into account the $\mathcal{Z}_2$-vortices. Therefore $T_{Neel}$ is estimated using the Monte-Carlo result for the 2D correlation length [10] which has a Kosterlitz-type behavior near the temperature $T_{KT}$ where the vortices are activated.