Monte Carlo study of the two-dimensional spin-1/2 quantum Heisenberg model: Spin correlations in La/sub 2/CuO/sub 4/

Journal Article · Sun Jan 01 04:00:00 EST 1989 · Phys. Rev. B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.39.575· OSTI ID:6441449

Manousakis, E; Salvador, R

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 La/sub 2/CuO/sub 4/, 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) Neel temperature T/sub N/approx.200 K are consistent with the experimental findings. In order to obtain agreement close to the Neel temperature, however, we need to introduce an interlayer coupling between the CuO/sub 2/ planes. The effect on a 3D coupling is only discussed in the framework of the quantum mechanical nonlinear sigma model in three space dimensions. For the case of La/sub 2/CuO/sub 4/ we find that close to T/sub N/ the sigma model in 3+1 dimensions reduces to the classical 3D Heisenberg model whose critical properties are known and fit the neutron-scattering data for Tapprox.T/sub N/.

• Research Organization: Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306
• OSTI ID: 6441449
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Journal Name: Phys. Rev. B: Condens. Matter; (United States) Vol. 39:1; ISSN PRBMD
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360204* -- Ceramics
Cermets
& Refractories-- Physical Properties
ANTIFERROMAGNETISM
COHERENT SCATTERING
COPPER COMPOUNDS
CRYSTAL MODELS
CUPRATES
DIFFRACTION
FERROMAGNETISM
HEISENBERG MODEL
LANTHANUM COMPOUNDS
MAGNETISM
MATHEMATICAL MODELS
MONTE CARLO METHOD
NEEL TEMPERATURE
NEUTRON DIFFRACTION
OXYGEN COMPOUNDS
PHYSICAL PROPERTIES
RAMAN EFFECT
RARE EARTH COMPOUNDS
SCATTERING
SERIES EXPANSION
SIMULATION
THERMODYNAMIC PROPERTIES
TRANSITION ELEMENT COMPOUNDS
TRANSITION TEMPERATURE
TWO-DIMENSIONAL CALCULATIONS