Numerical solution for the ground-state energy of the anisotropic Heisenberg model

1997 ◽  
Vol 62 (1) ◽  
pp. 13-21 ◽  
Author(s):  
P. Bracken
Keyword(s):  
Numerical Solution ◽  
Ground State Energy ◽  
Ground State ◽  
Heisenberg Model ◽  
State Energy ◽  
Anisotropic Heisenberg Model

GROUND-STATE PROPERTIES OF THE SPIN-1/2 ANTIFERROMAGNETIC HEISENBERG MODEL ON A CUBIC LATTICE BY A MONTE CARLO METHOD

1995 ◽  
Vol 09 (10) ◽  
pp. 619-627 ◽  
Author(s):  
R. A. SAUERWEIN ◽  
M. J. DE OLIVEIRA
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ground State Energy ◽  
Ground State ◽  
Heisenberg Model ◽  
State Energy ◽  
Isotropic Case ◽  
Spatial Anisotropy ◽  
Cubic Lattice ◽  
Antiferromagnetic Heisenberg Model

The spin-1/2 antiferromagnetic Heisenberg model with spatial anisotropy is studied on a cubic lattice by a Monte Carlo Method. Two types of spatial anisotropies are considered: planar and axial. The staggered magnetization m† and the ground state energy per site ∊0 are obtained as a function of the anisotropy. In the isotropic case we have obtained m† = 0.429 ± 0.001 in units where the saturated value is 0.5 and ∊0 = –0.899 ± 0.001.

GROUND-STATE ENERGY OF THE SPIN-1/2 TWO-DIMENSIONAL ANTIFERROMAGNETIC HEISENBERG MODEL

1989 ◽  
Vol 03 (09) ◽  
pp. 1443-1446 ◽  
Author(s):  
C.Y. PAN
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Heisenberg Model ◽  
State Energy ◽  
Finite Size ◽  
Group Method ◽  
Two Dimensional ◽  
Real Space Renormalization Group ◽  
Antiferromagnetic Heisenberg Model ◽  
Good Agreement

The ground-state energy of the spin-1/2 two-dimensional antiferromagnetic Heisenberg model is obtained by a real space renormalization group method. A relative larger cluster (5×5) is used to improve the accuracy and a boundary theory is applied to extrapolate to the result which is in good agreement with the finite-size calculation and in fairly good agreement with the other available numerical estimates. How to further improve the calculation is discussed.

scholarly journals Staggered Magnetisation in the Heisenberg Antiferromagnet

1994 ◽  
Vol 47 (2) ◽  
pp. 137 ◽  
Author(s):  
Lloyd CL Hollenberg ◽  
Michael J Tomlinson
Keyword(s):  
Magnetic Field ◽  
Energy Density ◽  
Ground State Energy ◽  
Ground State ◽  
Heisenberg Model ◽  
State Energy ◽  
Diagonal Form ◽  
Heisenberg Antiferromagnet ◽  
Matrix Elements ◽  
Weak Fields

In the presence of a staggered magnetic field, the plaquette expansion of the Lanczos matrix elements are obtained for the antiferromagnetic 2D Heisenberg model up to order 1/Np (Np is the number of plaquettes on the lattice). The resulting approximate tri-diagonal form of the Hamiltonian is diagonalised for various values of the field strength in the -> 00 limit for the ground state energy density. From the behaviour of the ground-state energy density at weak fields, the staggered magnetisation at this order in the plaquette expansion is found to be 0�71 (in units where the Neel state staggered magnetisation is 1� 0).

The ground state energy of the ±J spin glass from the genetic algorithm

1994 ◽  
Vol 4 (9) ◽  
pp. 1281-1285 ◽  
Author(s):  
P. Sutton ◽  
D. L. Hunter ◽  
N. Jan
Keyword(s):  
Genetic Algorithm ◽  
Spin Glass ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy
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