Vortex condensation in two-dimensional non-abelian spin models

We study by Monte Carlo simulation a family of two-dimensional models of coupled 'matter' S and gauge sigma = +- 1 fields. As the gauge coupling lambda varies, the model interpolates between the Heisenberg (lambda = infinity) and P2 (lambda = 0) models. We present evidence for vortex condensation at finite temperatures Tsub(C)(lambda), below which the thermodynamic functions have the same behavior as those of the Heisenberg model. For a range of lambda values a first-order transition is found at Tsub(c)(lambda). Since similar results were found for the same model with XY spins known to have a Kosterlitz-Thouless transition, we cannot rule out the existence of an infinite-order transition at Tsub(c)(lambda) for the model with three component spins. (orig.)