Series expansions from the finite lattice method

1977 ◽  
Vol 10 (5) ◽  
pp. 801-805 ◽  
Author(s):  
T de Neef ◽  
I G Enting
Keyword(s):  
Finite Lattice ◽  
Series Expansions ◽  
Lattice Method

scholarly journals Some Algebraic Techniques for obtaining Low-temperature Series Expansions

1978 ◽  
Vol 31 (6) ◽  
pp. 515 ◽  
Author(s):  
IG Enting
Keyword(s):  
Low Temperature ◽  
Statistical Mechanics ◽  
Series Expansion ◽  
General Result ◽  
Generating Functions ◽  
Finite Lattice ◽  
Lattice Models ◽  
Temperature Series ◽  
Series Expansions ◽  
Lattice Method

It is shown that low-temperature series expansions for lattice models in statistical mechanics can be obtained from a consideration of only connected strong subgraphs of the lattice. This general result is used as the basis of a linked-cluster form of the method of partial generating functions and also as the basis for extending the finite lattice method of series expansion to low-temperature series.

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.

Variational study on the ground state of the spin XY magnet

1978 ◽  
Vol 56 (7) ◽  
pp. 902-912 ◽  
Author(s):  
Masuo Suzuki ◽  
Seiji Miyashita
Keyword(s):  
Wave Function ◽  
Variational Method ◽  
Ground State ◽  
State Energy ◽  
Finite Lattice ◽  
Long Range Order ◽  
Lattice Method ◽  
Approximate Wave Function ◽  
Approximate Wave ◽  
Variational Study

An approximate wave function of the ground state of the spin [Formula: see text] XY magnet is derived using a variational method. This wave function yields estimates of the ground state energy and long-range order which agree very well with the results obtained by Betts and Oitmaa by a finite lattice method.

scholarly journals The Coupled Cluster Method Applied to the Spin-Half XXZ Model on the Honeycomb Lattice

1998 ◽  
Vol 12 (23) ◽  
pp. 2371-2383 ◽  
Author(s):  
R. F. Bishop ◽  
J. Rosenfeld
Keyword(s):  
Ground State ◽  
State Energy ◽  
Finite Lattice ◽  
Approximation Schemes ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Series Expansions ◽  
Honeycomb Lattice ◽  
Coupled Cluster Method ◽  
Xxz Model

The coupled cluster method (CCM) is applied to the spin-half XXZ model on the honeycomb lattice. Hierarchical CCM approximation schemes are applied in order to obtain the ground-state properties. The possible critical behavior of this model is also examined. Reasonably good results for the ground-state energy and the staggered magnetization are obtained, in comparison to the results from Monte Carlo simulations, spin-wave techniques, series expansions, and finite lattice diagonalizations, that have already been performed on this model.

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