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

Abstract

We obtain precise values for the fugacities of vortices in the 2d planar rotor model from Monte Carlo simulations in the sector with no vortices. The bare spin-wave stiffness is also calculated and shown to have significant anharmonicity. Using these as inputs in the KT recursion relations, we predict 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 commences in the unconstrained system. The latter value, being in excellent agreement with all recent determinations of T_c, demonstrates that our method 1) constitutes a stringent measure of the relevance of higher-order terms in KT theory and 2) can be used to obtain transition temperatures in similar systems with modest computational effort.