Writhe-induced knotting in a lattice polymer

We consider a simple lattice model of a topological phase transition in open polymers. To be precise, we study a model of self-avoiding walks on the simple cubic lattice tethered to a surface and weighted by an appropriately defined writhe. We also consider the effect of pulling the untethered end of the polymer from the surface. Regardless of the force we find a first-order phase transition which we argue is a consequence of increased knotting in the lattice polymer, rather than due to other effects such as the formation of plectonemes.