Neel Temperature of Quasi-Low-Dimensional Heisenberg Antiferromagnets

TL;DR

This paper calculates the Ne9el temperature of quasi-low-dimensional Heisenberg antiferromagnets using Monte Carlo simulations, revealing a universal relation for small inter-chain or inter-layer couplings and providing empirical formulas for experimental analysis.

Contribution

It introduces a modified RPA-like relation for Ne9el temperature with a universal renormalized coordination number for small couplings.

Findings

Ne9el temperature follows a modified RPA relation for small J'/J.

Universal renormalized coordination number is independent of spin size.

Provides empirical formulas for experimental data analysis.

Abstract

The N\'eel temperature, $T_{\rm N}$, 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 $J'/J$ down to $J'/J\simeq 10^{-3}$. We find that $T_{\rm N}$ obeys a modified random-phase approximation-like relation for small $J'/J$ with an effective universal renormalized coordination number, independent of the size of the spin. Empirical formulae describing $T_{\rm N}$ for a wide range of $J'$ and useful for the analysis of experimental measurements are presented.