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 θ-polymers at the critical point [10]. A common model for the collapse transition of polymers is a lattice self-avoiding walk with a nearest neighbour attraction [10, 38]. 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 [40]. 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 θ-transition in walks with nearestneighbour contacts. This places our models in a different universality class from the θ-transition in collapsing self-avoiding walks.