Monte Carlo study of the two-dimensional spin-1/2quantum Heisenberg model: Spin correlations in
- 1 January 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 39 (1), 575-585
- https://doi.org/10.1103/physrevb.39.575
Abstract
We study the spin-1/2 quantum ferromagnetic and antiferromagnetic Heisenberg model using Handscomb’s Monte Carlo (MC) method on square lattices of various sizes. As the temperature is lowered the calculated correlation length in the antiferromagnetic case grows more rapidly than in the ferromagnetic case. We also obtain the correlation length in the leading order of the high-temperature series expansion which, at high temperatures, agrees very well with the MC results. The correlation length obtained from the MC calculation for the ferromagnetic and antiferromagnetic case is compared with existing theories. Taking the average value for the antiferromagnetic coupling between the values suggested by neutron- and Raman-scattering experiments done on , we compare our results for the correlation length with those observed by the neutron-scattering experiments. We find that our results for the correlation lengths away from the three-dimensional (3D) Néel temperature ∼200 K are consistent with the experimental findings. In order to obtain agreement close to the Néel temperature, however, we need to introduce an interlayer coupling between the planes. The effect on a 3D coupling is only discussed in the framework of the quantum mechanical nonlinear σ model in three space dimensions. For the case of we find that close to the σ model in 3+1 dimensions reduces to the classical 3D Heisenberg model whose critical properties are known and fit the neutron-scattering data for T∼.
Keywords
This publication has 31 references indexed in Scilit:
- Static and dynamic spin correlations in pure and dopedPhysical Review B, 1988
- Dynamics of spin fluctuations in lanthanum cupratePhysical Review B, 1988
- Two-dimensional antiferromagnetic quantum spin-fluid state inPhysical Review Letters, 1987
- Resonating–valence-bond theory of phase transitions and superconductivity in-based compoundsPhysical Review Letters, 1987
- Antiferromagnetism inPhysical Review Letters, 1987
- Bulk superconductivity at 36 K inPhysical Review Letters, 1987
- Evidence for superconductivity above 40 K in the La-Ba-Cu-O compound systemPhysical Review Letters, 1987
- High TcSuperconductivity of La-Ba-Cu OxidesJapanese Journal of Applied Physics, 1987
- Possible highT c superconductivity in the Ba?La?Cu?O systemZeitschrift für Physik B Condensed Matter, 1986
- Attractive Interaction and Pairing in Fermion Systems with Strong On-Site RepulsionPhysical Review Letters, 1985