Spin exchange in quantum rings and wires in the Wigner-crystal limit
  We present a controlled method for computing the exchange coupling in strongly correlated one-dimensional electron systems. It is based on the asymptotically exact relation between the exchange constant and the pair-correlation function of spinless electrons. Explicit results are obtained for thin quantum rings with realistic Coulomb interactions, by calculating this function via a many-body instanton approach. 
Michael M. Fogler and Eugene Pivovarov