The writhe of polygons on the face-centred cubic lattice

Citation
M. Garcia et al., The writhe of polygons on the face-centred cubic lattice, J PHYS A, 32(25), 1999, pp. 4593-4600
Citations number
13
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
32
Issue
25
Year of publication
1999
Pages
4593 - 4600
Database
ISI
SICI code
0305-4470(19990625)32:25<4593:TWOPOT>2.0.ZU;2-B
Abstract
For polygons on the simple cubic lattice there is an important theorem due to Lacher and Sumners which shows that the writhe of a polygon is the avera ge of the linking numbers of the polygon and its pushoffs in four particula r directions. This implies that the writhe of a polygon on the simple cubic lattice is always rational. We prove a related theorem for the face-centre d cubic (fcc) lattice but show that, on this lattice, the probability that a polygon of length n has irrational writhe tends to unity as n tends to in finity. In addition, we show that the expectation of the absolute value of the writhe increases at least as fast as root n for large n.