Behavior of polymer end-to-end distance in two dimensions at the theta point

The end-to-end distance of a flexible polymer in a theta solvent in two dimensions is investigated. A mean field theory is presented which predicts significant deviations from ideal behavior at the theta point. A real space renormalization group approach is employed to investigate further the behavior of the polymer’s end-to-end distance at the theta point and to elucidate the analogy with thermodynamic tricritical behavior. Our results suggest that the correct result may be numerically closer to the mean prediction than to the values obtained from second order ε = (3−d) expansions of field theory models of critical phenomena.