Defect fugacity, spin-wave stiffness and T-c of the 2d planar rotor model

We obtain precise values for the fugacities of vortices in the 2d planar ro tor model from Monte Carlo simulations in the sector with no vortices. The bare spin-wave stiffness is also calculated and shown to have significant a nharmonicity. Using these as inputs in the KT recursion relations, we predi ct the temperature T-c = 0.925, using linearised equations, and T-c = 0.899 +/- 0.005 using next higher-order corrections, at which vortex unbinding c ommences in the unconstrained system. The latter value, being in excellent agreement with all recent determinations of T-c, demonstrates that our meth od 1) constitutes a stringent measure of the relevance of higher-order term s in KT theory and 2) can be used to obtain transition temperatures in simi lar systems with modest computational effort.