Linking and link complexity of geometrically constrained pairs of rings

We investigate and compare the effects of two different constraints on the geometrical properties and linking of pairs of polygons on the simple cubic lattice, using Monte Carlo methods. One constraint is to insist that the centres of mass of the two polygons are less than distance $d$ apart, and the other is to insist that the radius of gyration of the \emph{pair} of polygons is less than $R$. The second constraint results in links that are quite spherically symmetric, especially at small values of $R$, while the first constraint gives much less spherically symmetric pairs, prolate at large $d$ and becoming more oblate at smaller $d$. These effects have an influence on the observed values of the linking probability and link spectrum.