MAGNETIC MOMENT OF 2-DIMENSIONAL AND 3-DIMENSIONAL MANY-ELECTRON SYSTEMS EXAMINED WITH DEPENDENCE ON A COMMON SIZE PARAMETER

2002 ◽  
Vol 16 (30) ◽  
pp. 1183-1191
Author(s):  
S. OLSZEWSKI
Keyword(s):  
Magnetic Moment ◽  
Magnetic Moments ◽  
Electron Gas ◽  
Three Dimensional ◽  
Electron Systems ◽  
Size Parameter ◽  
3 Dimensional ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
The Moment

The orbital magnetic moments induced by a constant magnetic field in a two-dimensional (2D) and three-dimensional (3D) electron gas are calculated on the same footing independent of the conventional method based on statistical thermodynamics. The dependence of the moment on a common size parameter — defined as the cubic root of the volume occupied by one electron in a 3D gas — is found to be a similar monotonic function for both kinds of electron gas. This monotonic dependence is compared with the oscillating function of the size parameter obtained for the magnetic moment calculated in the case of a 2D slice of the tightly-bound s-electron states in a simple-cubic, or body-centred cubic, lattice.

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.

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.

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.

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 Microscopic Theory of Multipole Ordering in f-Electron Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Takashi Hotta
Keyword(s):  
Random Phase Approximation ◽  
Random Phase ◽  
Three Dimensional ◽  
Microscopic Theory ◽  
Prototype Model ◽  
Spin Orbit Coupling ◽  
Electron Systems ◽  
Standard Quantum ◽  
Simple Cubic ◽  
Strong Spin

A microscopic framework to determine multipole ordering in f-electron systems is provided on the basis of the standard quantum field theory. For the construction of the framework, a seven-orbital Hubbard Hamiltonian with strong spin-orbit coupling is adopted as a prototype model. A type of multipole and ordering vector is determined from the divergence of multipole susceptibility, which is evaluated in a random phase approximation. As an example of the application of the present framework, a multipole phase diagram on a three-dimensional simple cubic lattice is discussed for the case of n=2, where n denotes the average f-electron number per site. Finally, future problems concerning multipole ordering and fluctuations are briefly discussed.

Waves in three-dimensional simple cubic lattice

2006 ◽  
Vol 30 (4) ◽  
pp. 909-919 ◽  
Author(s):  
Xiao-yun Wang ◽  
Wen-shan Duan ◽  
Mai-mai Lin ◽  
Gui-xin Wan
Keyword(s):  
Three Dimensional ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

scholarly journals INDUCED MAGNETIC MOMENTS IN THREE-DIMENSIONAL GAUGE THEORIES WITH EXTERNAL MAGNETIC FIELDS

1998 ◽  
Vol 13 (22) ◽  
pp. 1765-1779 ◽  
Author(s):  
NICK E. MAVROMATOS ◽  
ARSHAD MOMEN
Keyword(s):  
Magnetic Fields ◽  
Magnetic Moment ◽  
Degrees Of Freedom ◽  
Magnetic Moments ◽  
Three Dimensional ◽  
Landau Levels ◽  
Three Dimensions ◽  
Effective Theory ◽  
Moment Interaction ◽  
Field Theoretical Model

We study the appearance of induced parity-violating magnetic moment, in the presence of external magnetic fields, for even-number of fermion species coupled to dynamical fields in three dimensions. Specifically, we use an SU(2) × U(1) gauge model for dynamical gauge symmetry breaking, which has also been proposed recently as a field theoretical model for high-Tc superconductors. By decomposing the fermionic degrees of freedom in terms of Landau levels, we show that, in the effective theory with the lowest Landau levels, a parity-violating magnetic moment interaction is induced by the higher Landau levels when the fermions are massive. The possible relevance of this result for a recently observed phenomenon in high-T c superconductors is also discussed.

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