Asymptotics of linked polygons

The asymptotic (i.e. large n) behaviour of pairs of ring polymers can depend on whether or not they are topologically linked and on the link complexity. We study this problem for pairs of linked polygons on the simple cubic lattice using a Monte Carlo method that, by keeping the link type fixed, can sample pairs of polygons whose individual lengths can fluctuate. By considering different prime links and linked pairs with knotted components we study how the link complexity affects the connective constant and the entropic exponent of these systems. We present numerical evidence that, in the large n limit, the entropically favoured situation corresponds to one component growing with n while the second component (and so the linked portion) has contour length o(n). (paper)