BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices
E J Janse van Rensburg, Andrew Rechnitzer · Journal of Physics A Mathematical and Theoretical · 2011
In this paper, the elementary moves of the BFACF-algorithm (Aragão de Carvalho and Caracciolo 1983 Phys. Rev. B 27 1635–45, Aragão 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.