Neel Temperature of Quasi-Low-Dimensional Heisenberg Antiferromagnets

Abstract

The Néel temperature, $T_{\mathrm{N}}$, of quasi-one- and quasi-two-dimensional antiferromagnetic Heisenberg models on a cubic lattice is calculated by Monte Carlo simulations as a function of inter-chain (inter-layer) to intra-chain (intra-layer) coupling $J^{\prime }/J$ down to $J^{\prime }/J\simeq 10^{-3}$. We find that $T_{\mathrm{N}}$ obeys a modified random-phase approximation-like relation for small $J^{\prime }/J$ with an effective universal renormalized coordination number, independent of the size of the spin. Empirical formulae describing $T_{\mathrm{N}}$ for a wide range of $J^{\prime }$ and useful for the analysis of experimental measurements are presented.

4 pages, 4 figures, to be published in Phys. Rev. Lett