Possible temperature marginality in the two-dimensionalS=12XYmodel by a linear renormalization transformation

A real-space linear renormalization transformation is proposed for studying the critical properties of the two-dimensional spin-½ $\mathrm{XY}$ model on the triangular lattice. The results of various approximations suggest a critical behavior of the same kind as that predicted by other theories and approaches for the classical case. The imposition of marginality for temperature deviations from criticality leads to an almost marginal secondary eigenoperator and to magnetic critical parameters which are not far from currently proposed values for the classical model.