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

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.