# Abstract

We discuss the unusual critical behavior of a generalized XY model containing both $$2\pi$$-periodic and $$\pi$$-periodic couplings between sites, allowing for ordinary vortices and half-vortices. The phase diagram of this system includes both 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.