scholarly journals Extension to orderβ23of the high-temperature expansions for the spin-12Ising model on simple cubic and body-centered cubic lattices

2000 ◽  
Vol 62 (22) ◽  
pp. 14837-14843 ◽  
Author(s):  
P. Butera ◽  
M. Comi
Keyword(s):  
High Temperature ◽  
Body Centered Cubic ◽  
Cubic Lattices ◽  
Simple Cubic

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.

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.

scholarly journals High-temperature Thermodynamics of the Hubbard Model

1993 ◽  
Vol 46 (5) ◽  
pp. 613
Author(s):  
J Oitmaa ◽  
JA Henderson
Keyword(s):  
High Temperature ◽  
Hubbard Model ◽  
Specific Heat ◽  
High Temperatures ◽  
Padé Approximants ◽  
Numerical Results ◽  
Strongly Correlated ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Atomic Limit

Recently derived 10th-order high-temperature expansions for the Hubbard model are used to obtain the ferromagnetic susceptibility and specific heat at high temperatures. Numerical results are obtained for the simple cubic and face-centred cubic lattices by using Pade approximants to sum the series. The results are compared with two solvable limiting cases, namely the non-interacting limit U = 0 and the strongly-correlated or atomic limit t = O.

The spin XY model. V. Moments of the spin–spin correlations in three dimensions

1980 ◽  
Vol 58 (11) ◽  
pp. 1651-1657 ◽  
Author(s):  
D. D. Betts ◽  
E. W. Grundke
Keyword(s):  
High Temperature ◽  
Three Dimensions ◽  
Transverse Spin ◽  
Xy Model ◽  
Spin Correlations ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Text Model ◽  
Critical Amplitudes

Ninth degree high temperature expansions have been obtained for all transverse spin–spin correlations of the [Formula: see text] model on the simple cubic and body centred cubic lattices. Analysis of the series for the second and fourth moments of the correlations yields the estimate of v = 0.689 ± 0.010 and estimates of critical amplitudes. No evidence for violation of hyperscaling is found.

High-temperature properties of the Ising model on the cristobalite lattice

1968 ◽  
Vol 46 (8) ◽  
pp. 971-975 ◽  
Author(s):  
D. D. Betts ◽  
R. V. Ditzian
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Curie Temperature ◽  
Coordination Number ◽  
Critical Energy ◽  
Critical Parameters ◽  
High Temperature Properties ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Effect Of Structure

The high-temperature properties of the Ising model on the cristobalite lattice are investigated by series expansion methods. The Curie temperature is found to be vl = tanh J/kTl = 0.2330 ± 0.003, the amplitude of the singularity in the susceptibility is Γ = 1.100 ± 0.001, the critical energy is −Ec/kTc = 0.268 ± 0.006, and the critical entropy is Sc/k = 0.548 ± 0.003. A comparison of critical parameters for the cristobalite and simple cubic lattices allows one to see the effect of structure for two lattices of the same coordination number.

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