CRITICAL TEMPERATURES AND MEAN-FIELD CRITICAL COEFFICIENTS FOR THE HEISENBERG MODEL BASED ON CVM

1992 ◽  
Vol 06 (13) ◽  
pp. 2363-2374
Author(s):  
GIICHI TANAKA ◽  
MINORU KIMURA
Keyword(s):  
Heisenberg Model ◽  
Mean Field ◽  
Three Dimensional ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Critical Temperatures ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Cluster Variation

Critical temperatures T c and mean-field critical coefficients [Formula: see text] for susceptibilities are calculated by a cluster-variation method (CVM) for a three-dimensional Heisenberg model on a simple cubic lattice. Both the full CVM based on a 4-spin cluster and the SCVM are applied and the same values for T c and [Formula: see text] are obtained by three different approximation in the SCVM. The results are compared with those obtained by the same approach for the three-dimensional Ising model on the simple cubic lattice.

scholarly journals Effect of Anisotropy on the Critical Behaviour of Three- Dimensional Heisenberg Ferromagnets

1976 ◽  
Vol 31 (1) ◽  
pp. 34-40 ◽  
Author(s):  
R. Shanker ◽  
R. A. Singh
Keyword(s):  
Three Dimensional ◽  
Experimental Investigations ◽  
Isotropic Case ◽  
Zero Field ◽  
Critical Temperatures ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Anisotropic System ◽  
Critical Temperature Tc

The anisotropic nearest-neighbour Heisenberg model for the simple cubic lattice has been investigated by interpolating the anisotropy between the Ising and isotropic Heisenberg limits via general spin high-temperature series expansions of the zero-field suspectibility. This is done by estimating the critical temperature (Tc(3)) and the susceptibility exponent γ from the analysis of the series by the Ratio and Pade approximants methods. It is noted that Tc(3) varies with anisotropy while γ is almost the same for the anisotropic system, and a jump in it occurs for the isotropic case in agreement with the universality hypothesis. The effect of anisotropy on the susceptibility is also shown. Further, it is seen that estimates of γ for the two extreme limits agree well with those of previous theoretical as well as experimental investigations. In addition, critical temperatures have been summarised in a relation, and expressions for the magnetisation have been derived.

scholarly journals Phase transition induced by an external field in a three-dimensional isotropic Heisenberg antiferromagnet

2018 ◽  
Vol 32 (32) ◽  
pp. 1850390
Author(s):  
Minos A. Neto ◽  
J. Roberto Viana ◽  
Octavio D. R. Salmon ◽  
E. Bublitz Filho ◽  
José Ricardo de Sousa
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Three Dimensional ◽  
Effective Field ◽  
The Body ◽  
Bravais Lattice ◽  
Body Centered Cubic ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic

The critical frontier of the isotropic antiferromagnetic Heisenberg model in a magnetic field along the z-axis has been studied by mean-field and effective-field renormalization group calculations. These methods, abbreviated as MFRG and EFRG, are based on the comparison of two clusters of different sizes, each of them trying to mimic a specific Bravais lattice. The frontier line in the plane of temperature versus magnetic field was obtained for the simple cubic and the body-centered cubic lattices. Spin clusters with sizes N = 1, 2, 4 were used so as to implement MFRG-12, EFRG-12 and EFRG-24 numerical equations. For the simple cubic lattice, the MFRG frontier exhibits a notorious re-entrant behavior. This problem is improved by the EFRG technique. However, both methods agree at lower fields. For the body-centered cubic lattice, the MFRG method did not work. As in the cubic lattice, all the EFRG results agree at lower fields. Nevertheless, the EFRG-12 approach gave no solution for very low temperatures. Comparisons with other methods have been discussed.

Resistance calculation of the decorated centered cubic networks: Applications of the Green's function

2014 ◽  
Vol 28 (32) ◽  
pp. 1450252 ◽  
Author(s):  
M. Q. Owaidat ◽  
J. H. Asad ◽  
J. M. Khalifeh
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Three Dimensional ◽  
Numerical Results ◽  
Effective Resistance ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Simple Cubic Lattice

The effective resistance between any pair of vertices (sites) on the three-dimensional decorated centered cubic lattices is determined by using lattice Green's function method. Numerical results are presented for infinite decorated centered cubic networks. A mapping between the resistance of the edge-centered cubic lattice and that of the simple cubic lattice is shown.

Sign in / Sign up

Export Citation Format

Share Document