We have investigated the thermodynamics of the square lattice planar rotator model. By calculating a variety of thermodynamic quantities for the planar rotator model on a sequence of one-dimensional geometries using transfer functions, we find evidence that the square lattice model exhibits an ordinary thermodynamic phase transition, with power-law singularities in the thermodynamics described by the usual set of critical exponents. This is in contrast to the widely-held view that the phase transition in the model should be of the Kosterlitz-Thouless type. We have constructed a Hubbard-type model of bilayer strontium ruthenate Sr₃Ru₂O₇. We find that the HartreeFock mean field solution of our model can be made to exhibit a metamagnetic jump that matches that seen in Sr₃Ru₂O₇, and this is clearly associated with a certain quasi one-dimensional feature in the electronic structure. We therefore suggest that this is the origin of the metamagnetism in Sr₃Ru₂O₇. The metamagnetism in our modelling is associated with a phase-separated mixture of low- and high-magnetisation solutions, which we suggest corresponds to the nematic phase in Sr₃Ru₂O₇.