The ground state of two quantum models of magnetism

1978 ◽  
Vol 56 (7) ◽  
pp. 897-901 ◽  
Author(s):  
J. Oitmaa ◽  
D. D. Betts
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Transverse Magnetization ◽  
Heisenberg Antiferromagnet ◽  
Pair Correlations ◽  
Quantum Models ◽  
Infinite Lattices

The ground state energy and pair correlations have been computed exactly for the spin [Formula: see text] XY magnet and isotropic Heisenberg antiferromagnet, for a sequence of finite cells on the square and honeycomb lattices. Precise estimates of the ground state energy of the infinite lattices are obtained by extrapolation. It is predicted that the XY magnet has a non-zero transverse magnetization and the Heisenberg antiferromagnet has a non-zero staggered magnetization in the ground state.

scholarly journals Magnetization process of the S = 1/2 Heisenberg antiferromagnet on the floret pentagonal lattice

2021 ◽  
Vol 5 (12) ◽  
pp. 125008
Author(s):  
Rito Furuchi ◽  
Hiroki Nakano ◽  
Norikazu Todoroki ◽  
Toru Sakai
Keyword(s):  
Magnetic Field ◽  
Saturation Magnetization ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Heisenberg Antiferromagnet ◽  
Magnetization Process ◽  
Diagonalization Method ◽  
The One ◽  
Peculiar Phenomenon

Abstract We study the S = 1/2 Heisenberg antiferromagnet on the floret pentagonal lattice by numerical diagonalization method. This system shows various behaviours that are different from that of the Cairo-pentagonal-lattice antiferromagnet. The ground-state energy without magnetic field and the magnetization process of this system are reported. Magnetization plateaux appear at one-ninth height of the saturation magnetization, at one-third height, and at seven-ninth height. The magnetization plateaux at one-third and seven-ninth heights come from interactions linking the sixfold-coordinated spin sites. A magnetization jump appears from the plateau at one-ninth height to the plateau at one-third height. Another magnetization jump is observed between the heights corresponding to the one-third and seven-ninth plateaux; however the jump is away from the two plateaux, namely, the jump is not accompanied with any magnetization plateaux. The jump is a peculiar phenomenon that has not been reported.

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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