  We explore the phase diagram of the SU(2) Yang-Mills theory in 5 dimensions
by numerical simulations. The lattice system shows a dimensionally-reduced
phase where the extra dimension is small compared to the four dimensional
correlation length. In the low-energy regime of this phase, the system behaves
like a four-dimensional gauge theory coupled to an adjoint scalar field. By
tuning the bare parameters of the lattice model, we identify lines of constant
physics, and analyse the behaviour of the non-perturbative scalar mass as a
function of the compactification and the cut-off scales. The perturbative
prediction that the effective theory contains a light particle with a mass that
is independent of the cut-off is tested against non-pertubative results.
