Ring polymer simulations with global radius of curvature

We simulate three-dimensional flexible off-lattice ring polymers of length L up to L=4000 for various values of the global radius of curvature R_grc=0.25, 0.48, and 1.0 and R_grc=2.0. We utilize two different ensembles: one with a δ-function constraint on the radius, and the other with a θ-function. For both cases the global radius of curvature provides a valid regularization of polymers with thickness D=2R_grc. The Flory-type critical exponent ν_SAW of self-avoiding rings at D=2 is found to be ν_SAW=0.5869(5) from the radii of gyration chain length scaling, while other D values produce consistent results. For our current implementation, the numerical effort of chain thickness calculations is bounded by a number O (L ln L) per single update. We also study low-temperature configurations of spatially dense Lennard-Jones homopolymers on a ring and identify some conformational building blocks.