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

摘要

In this paper the elementary moves of the BFACF-algorithm for latticepolygons are generalised to elementary moves of BFACF-style algorithms forlattice polygons in the body-centred (BCC) and face-centred (FCC) cubiclattices. We prove that the ergodicity classes of these new elementary movescoincide with the knot types of unrooted polygons in the BCC and FCC latticesand so expand a similar result for the cubic lattice. Implementations of thesealgorithms for knotted polygons using the GAS algorithm produce estimates ofthe minimal length of knotted polygons in the BCC and FCC lattices.