  We investigate the 2d XY model by using the constraint angle action, which
belongs to the class of topological lattice actions. These actions violate
important features usually demanded for a lattice action, such as the correct
classical continuum limit and the applicability of perturbation theory.
Nevertheless, they still lead to the same universal quantum continuum limit and
show excellent scaling behavior. By using the constraint angle action we gain
new insight into the Berezinskii-Kosterlitz-Thouless phase transition of the 2d
XY model. This phase transition is of special interest since it is one of the
few examples of a phase transition beyond second order. It is of infinite order
and therefore an essential phase transition. In particular, we observe an
excellent scaling behavior of the helicity modulus, which characterizes this
phase transition. We also observe that the mechanism of (un)binding
vortex--anti-vortex pairs follows the usual pattern, although free vortices do
not require any energy in the formulation of the 2d XY model using the
constraint angle action.
