Monte Carlo simulations of linear and cyclic chains on cubic and quadratic lattices

Abstract

A Monte Carlo algorithm for hypercubic lattices is investigated that combines end and kink reptations with local dynamic motions. It can be used for linear chains, for rings, and for the equilibration of the arms of star polymers. The algorithm fulfils the condition of detailed balance, and it is ergodic for a single linear chain. For the special case of a cyclic chain in two dimensions, a proof of ergodicity is also given. The statistical properties of the algorithm are discussed and, as examples, chain dimensions of linear and cyclic chains are computed