scholarly journals INTERNAL ENERGY OF HEISENBERG SPIN-1/2 J1 - J2 ANTIFERROMAGNET ON THE BODY-CENTERED-CUBIC LATTICE IN TYABLIKOV APPROXIMATION

2014 ◽  
Vol 5 (2) ◽  
Author(s):  
Мilan Pantić ◽  
Darko Kapor ◽  
Petar Mali ◽  
Milica Pavkov Hrvojević ◽  
Slobodan Radošević ◽  
...  
Keyword(s):  
Internal Energy ◽  
The Body ◽  
Body Centered Cubic ◽  
Stripe Phase ◽  
Heisenberg Spin ◽  
Sublattice Magnetization ◽  
Cubic Lattice ◽  
First Order Phase Transition ◽  
First Order Phase ◽  
Body Centered Cubic Lattice

Magnetic properties of spin ½ J1-J2 quantum Heisenberg antiferromagnet on body centered cubic lattice are investigated in the paper. By using two-time temperature Green's functions, sublattice magnetization and critical temperature depending on the frustration ratio J2/ J1 are obtained in both stripe and Neel phase. The analysis of ground state sublattice magnetization and internal energy indicates the first order phase transition from Neel to stripe phase for 0.7 J2/ J1 0.8, which is in agreement with previous studies.

MINIMAL KNOTTING NUMBERS

2009 ◽  
Vol 18 (08) ◽  
pp. 1159-1173 ◽  
Author(s):  
CASEY MANN ◽  
JENNIFER MCLOUD-MANN ◽  
RAMONA RANALLI ◽  
NATHAN SMITH ◽  
BENJAMIN MCCARTY
Keyword(s):  
The Body ◽  
Computer Algorithm ◽  
Face Centered Cubic ◽  
Body Centered Cubic ◽  
Cubic Lattice ◽  
The Face ◽  
Face Centered ◽  
Body Centered Cubic Lattice

This article concerns the minimal knotting number for several types of lattices, including the face-centered cubic lattice (fcc), two variations of the body-centered cubic lattice (bcc-14 and bcc-8), and simple-hexagonal lattices (sh). We find, through the use of a computer algorithm, that the minimal knotting number in sh is 20, in fcc is 15, in bcc-14 is 13, and bcc-8 is 18.

SOLID HARMONICS AS BASIS FUNCTIONS FOR CUBIC CRYSTALS

1959 ◽  
Vol 37 (3) ◽  
pp. 350-361 ◽  
Author(s):  
D. D. Betts
Keyword(s):  
Basis Functions ◽  
The Body ◽  
New Method ◽  
Face Centered Cubic ◽  
Body Centered Cubic ◽  
Cubic Crystals ◽  
Cubic Lattice ◽  
The Face ◽  
Face Centered ◽  
Body Centered Cubic Lattice

The various sets of basis functions useful in discussing cubic crystals must include sets of symmetrized combinations of powers of the co-ordinates ortho-gonalized over the cellular polyhedron. Such polynomials are here called solid harmonics. A study of the actual solid harmonics reveals the limitations of the spherical cell approximation. The solid harmonics can be used to develop a new method over the cellular polyhedron of the body-centered cubic lattice or of the face-centered cubic lattice.

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