Position-space renormalisation group for isolated polymer chains

Develops a cell position-space renormalisation group PSRG with which the authors study the scaling properties of isolated polymer chains. They model a chain by a self-avoiding walk constrained to a lattice. For rescaling factors b<or=6, they calculate recursion relations analytically on the square lattice with several different choices for the PSRG weight function. They also calculate implicit cell-to-cell transformations in which a cell of size b is rescaled to a cell of size b'. They also develop a constant-fugacity Monte Carlo method which enables them to simulate-in an unbiased way within the grand canonical ensemble-chains of up to 103 bonds. With this method they extend the PSRG to larger cells (b<or=150) on the square lattice. Their numerical method provides high statistical accuracy for all cell sizes.