Atmospheric collapse in self-avoiding walks: a numerical study using GARM

The coil-globule collapse of dilute linear polymers in a poor solvent is generally thought to be a second-order phase transition through theta-polymers at the critical point. A common model for the collapse transition of polymers is a lattice self-avoiding walk with a nearest neighbour attraction. In this paper we consider an alternative set of models for collapsing linear polymers. In particular, we simulate lattice walks weighted by an atmospheric statistic using the flatGARM algorithm. These models of walks undergo a collapse transition at a critical value of the parameters of the model. This transition appears to be discontinuous (first order), in contrast to the theta-transition in walks with nearest neighbour contacts. This places our models in a different universality class from the theta-transition in collapsing self-avoiding walks.