ABSTRACT
Chapter 15 deals with the pivot algorithm, which is a dynamic Monte Carlo (MC) method based on global moves. The main idea is the following: for an N-step self-avoiding walk on a square lattice, monomer k is selected at random (that is with probability 1/N) and a trial direction for step k is chosen at random with probability 1/4; then step k is temporarily changed to the trial direction, together with the part of the chain connected to it of monomers k + 1, k + 2,…,N + 1. If the excluded volume condition is satisfied, the trial move is accepted, otherwise it is rejected. The method is extremely efficient for SAWs in the bulk (N ~ 106), but very inefficient for chains under geometrical constraints. Also, due to the global moves, local structures of the chain might not be equilibrated, and if the energy is of interest, local moves should be added to the process. The efficiency of hybrid methods, enrichment/dimerization, and enrichment/RR described in Chapter 14 is also discussed.
