Antiferromagnetism in the Face-Centered Cubic Lattice. I. The Random-Phase Green's Function Approximation

1965 ◽  
Vol 139 (4A) ◽  
pp. A1304-A1312 ◽  
Author(s):  
M. E. Lines
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Approximation ◽  
Random Phase ◽  
Face Centered Cubic ◽  
Cubic Lattice ◽  
The Face ◽  
Face Centered

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.

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