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

TL;DR

This paper analyzes the Neel temperature and sublattice magnetization in a stacked triangular-lattice antiferromagnet using RG and Monte Carlo methods, highlighting limitations of RG in capturing vortex effects.

Contribution

It provides asymptotic formulas for Neel temperature and magnetization in weak interlayer coupling and incorporates Monte Carlo data to account for vortex phenomena.

Findings

RG approach is insufficient without vortex considerations.

Monte Carlo estimates improve Neel temperature predictions.

Asymptotic formulas are derived for weak interlayer coupling.

Abstract

The quantum Heisenberg antiferromagnet on the stacked triangular lattice with the intralayer nearest-neighbor exchange interaction J and interlayer exchange J' is considered within the non-linear $\sigma$-model with the use of the renormalization group (RG) approach. For J' << 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.