ON HOUSTON'S METHOD OF EVALUATING INTEGRALS OVER THE BRILLOUIN ZONE: NORMALIZATION FACTOR IN A SIMPLE CUBIC LATTICE

1962 ◽  
Vol 40 (9) ◽  
pp. 1153-1165 ◽  
Author(s):  
S. Ganesan ◽  
R. Srinivasan
Keyword(s):  
Brillouin Zone ◽  
Anisotropy Parameter ◽  
Face Centered Cubic ◽  
Normalization Procedure ◽  
Normalization Factor ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Face Centered

In evaluating integrals over the Brillouin zone by Houston's method, a normalization factor has to be used. A wave-vector-dependent normalization factor nj(q + Δq/2) is calculated by equating the volume common to a spherical shell of radius q and thickness Δq and the simple cubic Brillouin zone to the expression given by a j-direction Houston method. Some sample integrals are evaluated using this (GS) normalization procedure and Horton and Schiff's (HS) normalization procedure, originally developed for face-centered cubic lattices. The superiority of the GS method, especially with highly anisotropic functions, is demonstrated. From an evaluation of the moments of the frequency distribution function in a simple cubic lattice for various values of the anisotropy parameter, it is concluded that, when high accuracy is desired, the GS procedure is applicable over a wider range of anisotropy parameter than the HS procedure. The θ–T curve calculated by using the correct normalization procedure in a simple cubic lattice is in good agreement with that calculated by Blackman's method.

STUDY OF CRITICAL BEHAVIOUR IN DILUTED FERROMAGNETIC: THIN FILMS AND SEMI-INFINITES FILMS

2010 ◽  
Vol 24 (18) ◽  
pp. 3561-3596 ◽  
Author(s):  
R. MASROUR ◽  
M. HAMEDOUN ◽  
A. BENYOUSSEF
Keyword(s):  
Thin Film ◽  
Exchange Interaction ◽  
Exchange Interactions ◽  
Critical Value ◽  
Face Centered Cubic ◽  
Surface Exchange ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Face Centered

By using the high-temperature series expansion technique, we have analyzed the phase transition and the critical phenomena of a ferromagnetic thin film and ferromagnetic semi-infinite film, through three models: Ising, XY and Heisenberg. The critical reduced temperature τC(v) is studied as a function of the thickness of the film. In the case of the magnetic film and semi-infinite film, on the simple cubic lattice and the face-centered cubic lattice, τC(v) is studied as a function of the exchange interactions in the bulk, and on the surface. A critical value of the surface exchange interaction in the film above which the surface and the interface magnetism appears is obtained. The dependence of the reduced critical temperature on the thickness of the film has been investigated. These shifts of the critical temperatures TC(L) from the bulk value can be described by a power law. The obtained values for the simple cubic lattice and face centered cubic ferromagnetic thin film are in qualitative accordance with the universality class hypothesis. The critical exponent associated with the magnetic susceptibility is studied as a function of interactions. In a defined range of the exchange interactions, the obtained values for Heisenberg, XY and Ising models, for simple cubic thin film are comparable to the universal ones and are independent of the film thickness. The asymmetry of the structure and the competition of the effects of the exchange coupling, are important for the magnetic properties of the system. A critical value of the surface exchange interaction above which the surface magnetism appears is obtained. For the dependence of the critical parameter of surface reduced coupling [Formula: see text] as a function of the dilution x and the ratio of the exchange interaction between the surface and nearest neighbour layer to the bulk one R1 for the three studied models has been investigated. The magnetic phase diagrams are obtained for two structures. The percolation threshold is defined as the concentration xp at which τC=0. In the case of the thin film, the obtained values are xp≈0.2 in the bulk and xp≈0.4 at the surface. For the case of the semi-infinite film, the value obtained in the surface and the nearest layer at the surface is xp≈0.2.

Zero-Point Effects in Heisenberg Antiferromagnets with Arbitrary Range of Interaction

1972 ◽  
Vol 50 (23) ◽  
pp. 2991-2996 ◽  
Author(s):  
M. F. Collins ◽  
V. K. Tondon
Keyword(s):  
Ground State ◽  
State Energy ◽  
Correction Term ◽  
Zero Point ◽  
Face Centered Cubic ◽  
Heisenberg Antiferromagnet ◽  
Body Centered Cubic ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Face Centered

The ground state energy, spin-wave energy, and sublattice magnetization have been calculated for a Heisenberg antiferromagnet at the absolute zero of temperature. The treatment extends the earlier work of Anderson, Kubo, and Oguchi to apply for any two-sublattice antiferromagnet with arbitrary range of interaction. It is shown that for each exchange interaction there is a different characteristic correction term to the energies. Explicit calculations are made of these terms for the simple cubic, body-centered cubic, and face-centered cubic lattices, with both first- and second-neighbor interactions. Applications are also made to NiO and MnO. An extra term in the magnetization series beyond that given by earlier workers is derived.

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.

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