On the Divergence of the Perturbation Series for the Excluded-Volume Problem in Polymers. II. Collapse of a Single Chain in Poor Solvents

For a lattice polymer on the cubic lattice in three dimensional space, it is proved that a single polymer chain is contained in a small volume with probability 1 for negative real z, the measure of the strength of the intrachain interaction, when the polymer length becomes infinite with z being kept finite. The result suggests that the radii of convergence of the perturbation series so far obtained for a chain of finite length N are of order N^-1/2.