Semiflexible polymer in the cactus approximation

We investigate a cactus approximation for the analysis of a lattice polymer model (self-avoiding walk) in two and three dimensions. We focus on the semiflexible model, which incorporates both an attractive short range interaction between monomers that are nonconsecutive along the chain, and a bending energy (stiffness). In agreement with Monte Carlo simulations, we find two different qualitative behaviors. In the low stiffness regime the polymer undergoes two different transitions upon decreasing temperature: an ordinary Theta collapse from a swollen (''coil'') state to a disordered compact (''globule'') state, and then a first-order transition to an orientationally ordered (''anisotropic'') state. In the high stiffness regime the system displays a single first-order collapse from the coil state at high temperature to the anisotropic state at low temperature. We show that the cactus approximation is able to recover even fine qualitative features of the phase diagram, such as the stiffness dependence of the Theta temperature, with a relatively small computational effort.