Correlation Functions in the Fully Frustrated 2DXYModel

We present a detailed analysis of the critical properties of the two-dimensional XY model at full frustration. We calculate U(1) and ${\mathrm{Z}}_2$ gauge-invariant correlation functions, as well as the chiral magnetization and susceptibility, by using extensive Monte Carlo simulations in lattices up to 240×240. The best fits to our results give ${\nu }_{\mathrm{U}\left(1\right)\mathrm{}}$=0.3069, ${\mathrm{\eta }}_{\mathrm{U}\left(1\right)\mathrm{}}$(${\mathrm{T}}_{\mathrm{U}\left(1\right)\mathrm{}}^{\mathrm{c}}$=0.446)=0.1915, while ${\nu }_{{\mathrm{Z}}_2}$=0.875, 2${\mathrm{\beta }}_{{\mathrm{Z}}_2}$=0.1936, 2${\gamma }_{{\mathrm{Z}}_2}$=1.82, 2${\gamma }_{{\mathrm{Z}}_2}^{\prime }$=1.025. These novel results are quantitatively different from those expected for separate 2D XY and 2D Ising models.