Statistical Dynamics of Simple Cubic Lattices. Model for the Study of Brownian Motion

1960 ◽  
Vol 1 (4) ◽  
pp. 309-318 ◽  
Author(s):  
Robert J. Rubin
Keyword(s):  
Brownian Motion ◽  
Statistical Dynamics ◽  
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.

Invariance relations for random walks on simple cubic lattices

2006 ◽  
Vol 421 (1-3) ◽  
pp. 287-294 ◽  
Author(s):  
Roberto A. Garza-López ◽  
Anthony Linares ◽  
Alice Yoo ◽  
Greg Evans ◽  
John J. Kozak
Keyword(s):  
Random Walks ◽  
Cubic Lattices ◽  
Simple Cubic

Dispersion relation for two-dimensional simple cubic lattices

2008 ◽  
Vol 3 (2) ◽  
pp. 159-164 ◽  
Author(s):  
Dou-xiang Tian ◽  
Xiao-yun Wang ◽  
Cang-long Wang ◽  
Wen-shan Duan
Keyword(s):  
Dispersion Relation ◽  
Two Dimensional ◽  
Cubic Lattices ◽  
Simple Cubic
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