Monte Carlo simulations of the spin-(1/2 Heisenberg antiferromagnet on a square lattice

TLDR

The study simulates the spin‑½ antiferromagnetic square lattice to determine its ground‑state sublattice magnetization, motivated by links to oxide superconductor magnetism. Numerical simulations were performed on square lattices up to 12×12 spins to compute sublattice magnetization. The extrapolated staggered magnetization is 0.30 ± 0.02, significantly lower than earlier exact‑diagonalization results and consistent with spin‑wave theory and perturbation analyses.

Abstract

Motivated by the possible connection between superconductivity in the newly discovered oxide superconductors and the magnetic behavior of these materials, we have carried out numerical simulations to determine the sublattice magnetization ${m}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ in the ground state of the spin-(1/2 antiferromagnet on the square lattice with nearest-neighbor interactions. Lattices with N=L\ifmmode\times\else\texttimes\fi{}L spins, where L\ensuremath{\le}12, were used. Extrapolating our results for rotationally invariant correlation functions to the thermodynamic limit, we obtain a much smaller value than obtained previously by exact diagonalization on lattices with sizes up to N=16. For the staggered magnetization, we find ${m}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$=0.30\ifmmode\pm\else\textpm\fi{}0.02 in units where the saturation value is (1/2. This agrees with the result of spin-wave theory and a recent reanalysis of the perturbation expansion away from the Ising limit.