Renormalization-group approach to two-dimensional quantum models

Abstract

The two-dimensional $\mathrm{XY}$ and Heisenberg models are studied with a quantum-mechanical generalization of the Niemeijer and Van Leeuween renormalization-group method. In second-order cumulant expansion a fixed point exists for the $\mathrm{XY}$ model, giving a critical temperature at $\frac{J}{k{T}_{c}}\ensuremath{\cong}0.87\ifmmode\pm\else\textpm\fi{}0.05$. For the Heisenberg model we find a fixed point at ${K}^{*}=2.8$. This result may not be reliable, since the truncation of the cumulant expansion is only valid for small $K$.