PJLZ-gauge fixing approach in $SU(2)$ lattice gauge theory

We study the $SU(2)$ gauge theory with the interpolating gauge a la Parrinello–Jona-Lasinio–Zwanziger (PJLZ) with the gauge fixing functional $F=\sum_{x\mu} \frac{1}{2}\operatorname{Tr} (U_{x\mu}\sigma_3U_{x\mu}^{\dagger}\sigma_3)$. We find a strong indication of the non-analiticity with respect to the interpolating parameter $\lambda$ at $\lambda_c \sim 0.8$.