Phase diagrams of confined square lattice linked polygons

The phase diagrams of two models of two confined and dense two-dimensional ring polymers are examined numerically. The ring polymers are modeled by square lattice polygons in a square cavity and are placed to be either unlinked or linked in the plane. The phase diagrams of the two models are found to be a function of the placement of the ring polymers and include multicritical points where first-order and continuous phase boundaries meet. We estimate numerically the critical exponents associated with the phase boundaries and the multicritical points.