Collapse transition of linear polymers on a family of truncated n-simplex lattices

Abstract

We show that for linear polymers a collapse transition exists on a truncated six-simplex lattice but not on a truncated five-simplex lattice. The existence of the collapsed phase is determined not only by the connectivity but also by the geometrical form of the first-order unit of the fractal lattice. We report exact results for the critical exponents at the transition for the six-simplex lattice.