We develop a novel technique that allows us to directly probe the thermodynamics of the two dimensional limit of the nearest neighbour square lattice clock model. It is a process that uses exact diagonalisation techniques through the use of transfer functions. It is conceptually easy to understand as an extension of the transfer matrices used to solve the 1D Ising model and other similar Hamiltonians. This transfer function technique is applied to a set of 1D spiral geometries with increasing radius N. In the limit N → ∞ the spiral becomes the square lattice and our results are interpreted with respect to this limit. We present convincing evidence that the two transitions that are exhibited in the p > 4 clock model have singular behaviour and above a certain temperature between the transitions convergently behave like the plane rotator model.