  We discuss the unusual critical behavior of a generalized XY model containing
both 2\pi-periodic and \pi-periodic couplings between sites. The presence of
vortices and half-vortices allows for single-particle condensate and
pair-condensate phases. Using a field theoretic formulation and worm algorithm
Monte Carlo simulations, we show that in two dimensions it is possible for the
system to pass directly from the disordered (high temperature) phase to the
single particle (quasi)-condensate via an Ising transition, a situation
reminiscent of the `deconfined criticality' scenario.
