An $x-y$ model with nearest-neighbor interaction $V\left(\theta \right)=2J\{1-{\left[{cos}^2\right(\frac{\theta }{2}\left)\right]}^{p^2}\}$ is studied by Monte Carlo simulation. The model has a transition from a paramagnetic to an algebraic (massless) phase. An increase of the parameter $p$, which changes the shape of the potential, brings about a change in the nature of the transition from continuous to first order.

• Received 2 January 1984

DOI:https://doi.org/10.1103/PhysRevLett.52.1535