The critical pulling force for self-avoiding walks

Self-avoiding walks are a simple and well-known model of long, flexible polymers in a good solvent. Polymers being pulled away from a surface by an external agent can be modelled with self-avoiding walks in a half-space with a Boltzmann weight y associated with the pulling force. This model is known to have a critical point at a certain value yc of this Boltzmann weight, which is the location of a transition between the so-called free and ballistic phases. We prove that yc = 1, confirming conjectures based on numerical estimates by several authors.