Estimation of zero-temperature properties of quantum spin systems on the simple cubic lattice via exact diagonalization on finite lattices

1997 ◽  
Vol 75 (1) ◽  
pp. 47-66 ◽  
Author(s):  
D D Betts ◽  
G E Stewart
Keyword(s):  
Exact Diagonalization ◽  
Quantum Spin ◽  
Spin Systems ◽  
Zero Temperature ◽  
Quantum Spin Systems ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Finite Lattices

COHERENT-ANOMALY METHOD FOR QUANTUM SPIN SYSTEMS

1988 ◽  
Vol 02 (01) ◽  
pp. 1-11 ◽  
Author(s):  
NOBUYASU ITO ◽  
MASUO SUZUKI
Keyword(s):  
Critical Exponents ◽  
Heisenberg Model ◽  
Spontaneous Magnetization ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems ◽  
Cubic Lattice ◽  
Bethe Approximation ◽  
Simple Cubic ◽  
Simple Cubic Lattice

The coherent-anomaly method (CAM) is applied to the Heisenberg model to test the applicability of the CAM for quantum spin systems. The Weiss, Bethe and constant coupling approximations are tried for the Heisenberg model on the simple cubic lattice and estimate the critical exponents of the susceptibility and spontaneous magnetization using the CAM. The results show that the CAM is also powerful for quantum spin systems. The detailed results of the Bethe approximation of the spin-1/2 isotropic Heisenberg model are presented.

Improved finite-lattice method for estimating the zero-temperature properties of two-dimensional lattice models

1996 ◽  
Vol 74 (1-2) ◽  
pp. 54-64 ◽  
Author(s):  
D. D. Betts ◽  
S. Masui ◽  
N. Vats ◽  
G. E. Stewart
Keyword(s):  
Spontaneous Magnetization ◽  
Finite Lattice ◽  
Quantum Spin ◽  
Square Lattice ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Quantum Spin Systems ◽  
Lattice Method ◽  
Dimensional Lattice ◽  
Finite Lattices

The well-known finite-lattice method for the calculation of the properties of quantum spin systems on a two-dimensional lattice at zero temperature was introduced in 1978. The method has now been greatly improved for the square lattice by including finite lattices based on parallelogram tiles as well as the familiar finite lattices based on square tiles. Dozens of these new finite lattices have been tested and graded using the [Formula: see text] ferromagnet. In the process new and improved estimates have been obtained for the XY model's ground-state energy per spin, ε0 = −0.549 36(30) and spontaneous magnetization per spin, m = 0.4349(10). Other properties such as near-neighbour, zero-temperature spin–spin correlations, which appear not to have been calculated previously, have been estimated to high precision. Applications of the improved finite-lattice method to other models can readily be carried out.

Zero-temperature properties of quantum spin systems in two dimensions

1990 ◽  
Vol 68 (12) ◽  
pp. 1410-1418 ◽  
Author(s):  
D. D. Betts ◽  
S. Miyashita
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Magnetic Phase ◽  
Finite Lattice ◽  
Two Dimensions ◽  
Quantum Spin ◽  
Spin Systems ◽  
Heisenberg Antiferromagnet ◽  
Zero Temperature ◽  
Quantum Spin Systems

We consider the zero-temperature properties of four different spin 1/2 models on two-dimensional lattices: the XY ferromagnet, the XY antiferromagnet, the Heisenberg antiferromagnet, and the Dzyaloshinsky–Moriya models. Most of this article is a review of previously published work, but a few previously unpublished results are included. The relation between three of the models on bipartite lattices is described. The properties of the XY ferromagnet in two dimensions, especially those derived from extrapolation of finite lattice results, are reviewed. A numerical factor by which spin-wave and finite-lattice estimates of the long-range order parameter differ is discussed. For frustrated models on the triangular lattice the possibility of a chirality phase transition instead of, or in addition to, a magnetic phase transition is considered.

scholarly journals Quantum Spin Systems at Positive Temperature

2006 ◽  
Vol 269 (3) ◽  
pp. 611-657 ◽  
Author(s):  
Marek Biskup ◽  
Lincoln Chayes ◽  
Shannon Starr
Keyword(s):  
Quantum Spin ◽  
Spin Systems ◽  
Positive Temperature ◽  
Quantum Spin Systems

scholarly journals Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice

2014 ◽  
Vol 31 (7) ◽  
pp. 070503 ◽  
Author(s):  
Shun Wang ◽  
Zhi-Yuan Xie ◽  
Jing Chen ◽  
Bruce Normand ◽  
Tao Xiang
Keyword(s):  
Phase Transitions ◽  
Potts Models ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice
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