Searching for continuous phase transitions in 5D SU(2) lattice gauge theory

We study the phase diagram of 5-dimensional $SU(2)$ Yang-Mills theory on lattice. consider two extensions fundamental plaquette Wilson action in search for continuous transition suggested by $4+\epsilon$ expansion. The correspond to new terms action: i) a unit size adjoint representation or ii) two-unit sided square representation. use Monte Carlo sample first and second derivative entropy near confinement transition, with lattices up $12^{5}$. While we exclude presence order parameter space sampled model i), our data is not conclusive some regions ii).