Adsorbing staircase polygons subject to a force

We study several models of staircase polygons on the 45 degrees rotated square lattice, which interact with an impenetrable surface while also being pushed towards or pulled away from the surface by a force. The surface interaction is governed by a fugacity a and the force by a fugacity y. Staircase polygons are simplifications of more general self-avoiding polygons, a well-studied model of interacting ring polymers. For this simplified case we are able to exactly determine the limiting free energy in the full a-y plane, and demonstrate that staircase polygons exhibit four different phases, including a 'mixed' adsorbed-ballistic phase.