BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices

• Published in: Journal of physics. A, Mathematical and theoretical Vol. 44; no. 16; pp. 165001 - 25
• Main Authors: Janse van Rensburg, E J, Rechnitzer, A
• Format: Journal Article
• Language: English
• Published: IOP Publishing 22.04.2011
• Subjects: Algorithms; Body centered cubic lattice; Cubic lattice; Face centered cubic lattice; Knots; Lattices; Mathematical analysis; Polygons
• ISSN: 1751-8121; 1751-8113; 1751-8121
• DOI: 10.1088/1751-8113/44/16/165001

In this paper, the elementary moves of the BFACF-algorithm (Aragao de Carvalho and Caracciolo 1983 Phys. Rev. B 27 1635-45, Aragao de Carvalho and Caracciolo 1983 Nucl. Phys. B 215 209-48, Berg and Foester 1981 Phys. Lett. B 106 323-6) for lattice polygons are generalized to elementary moves of BFACF-style algorithms for lattice polygons in the body-centered (BCC) and face-centered (FCC) cubic lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC lattices and so expand a similar result for the cubic lattice (see Janse van Rensburg and Whittington (1991 J. Phys. A: Math. Gen. 24 5553-67)). Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC lattices.