Doping Dependence of the Néel Temperature in Mott-Hubbard Antiferromagnets: Effect of Vortices

The rapid destruction of long-range antiferromagnetic order upon doping of Mott-Hubbard antiferromagnetic insulators is studied within a generalized Berezinskii-Kosterlitz-Thouless renormalization group theory in accordance with recent calculations suggesting that holes dress with vortices. We calculate the doping-dependent Néel temperature in good agreement with experiments for high- $T_c$ cuprates. Interestingly, the critical doping where long-range order vanishes at zero temperature is predicted to be $x_c\sim 0.02$, independently of any energy scales of the system.