19-vertex version of the fully frustrated<i>XY</i>model

Abstract

We investigate a 19-vertex version of the two-dimensional fully frustrated XY (FFXY) model. We construct Yang-Baxter equations for this model and show that there is no solution. Therefore we have chosen a numerical approach based on the transfer matrix. The results show that a coupled XY Ising model is in the same universality class as the FFXY model. We find that the phase coupling over an Ising wall is irrelevant at criticality. This leads to a correction of earlier determinations of the dimension ${\mathit{x}}_{\mathit{h},\mathrm{I}\mathrm{s}}^{\mathrm{*}}$ of the Ising disorder operator. We find ${\mathit{x}}_{\mathit{h},\mathrm{I}\mathrm{s}}^{\mathrm{*}}$=0.123(5) and a conformal anomaly c=1.55(5). These results are consistent with the hypothesis that the FFXY model behaves as a superposition of an Ising model and an XY model. However, the dimensions associated with the energy, ${\mathit{x}}_{\mathit{t}}$=0.77(3), and with the XY magnetization ${\mathit{x}}_{\mathit{h},}$XY\ensuremath{\approxeq}0.17, refute this hypothesis.