ENTROPIC EXPONENTS OF LATTICE POLYGONS WITH SPECIFIED KNOT TYPE

Ring polymers in three dimensions can be knotted, and the dependence o f their critical behaviour on knot type is an open question. We study this problem for polygons on the simple cubic lattice using a novel gr and-canonical Monte Carlo method and present numerical evidence that t he entropic exponent depends on the knot type of the polygon. We conje cture that the exponent increases by unity for each additional factor in the knot factorization of the polygon.